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^70 


THE 
LONDON,  EDINBURGH,  and  DUBLIN 

PHILOSOPHICAL  MAGAZINE 

AND 

JOURNAL  OF  SCIENCE. 

CONDUCTED  BY 

SIR  ROBERT  KANE,  LL.D.  F.R.S.  M.R.LA.  P.C.S. 
SIR  WILLIAM  THOMSON,  Knt.  LL.D.  P.R.S.  &c. 

AND 

WILLIAM  FRANCIS,  Ph.D.  F.L.S.  P.R.A.S.  P.C.S. 


^'  Nee  araneuum  sane  iextas  ideo  mdior  quia  ex  se  flia  gignunt,  nee  notter 
Yilior  qnia  ex  alienis  libamiu  at  apes."    Just.  Lips.  P6^t»  lib.  i.  cap.  1 .  Not. 


VOL.  XLVIIL— FOURTH  SERIES. 
JULY— DECEMBER  1874. 


LONDON. 

TAYLOR  AND  FRANCIS,  RED  LION  COURT,  FLEET  STREET, 
Prffif«r«  and  Publishers  to  the  Universiiy  of  London  ; 

•OLD  BT  LONGMANS,  ORBSN,  RBADIB,  AND  Dm ;   KBNT  AND  CX>. ;   8IMPKIN,  NARSnALL, 

AND  00.  ;  AND  WniTTAKBR  AND  CO.  ; — A5D  BT  ADAM  AND  CHABLBS  BLACK, 

AND  THOMAS  CLARK,    BDINBUROH  ;    SMITH  AND  SON,  GLASGOW! — 

H0DGB8,    F08TBR,    AND    CO,    DUBLIN: — PUTNAM,    NBW 

YORK: — AND    ASHBR    AND    CO.,    BERLIN. 


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Meditationit  est  perscmtari  occulu;  contempUtionii  est  adminuri 

penpicua Admiratio  generat  qutestionem,  quettio  iiiTestigationem, 

invesdgatio  inventioiiem." — Hugo  de  S,  Vietore, 


— "  Cur  Spirent  venti,  cur  terra  dehiscat. 
Cur  mare  turgescat,  pelago  cur  tantus  amaror. 
Cur  caput  obscura  Phoebus  femigine  coudat. 
Quid  toties  diros  cogat  flagrare  cometas; 
Quid  pariat  nubes,  veniant  cur  fulmina  coelo, 
Quo  micet  igne  Iris,  superos  quis  conciat  orbes 
Tam  vario  motu." 

J.  B.  PinelU  ad  Masonimm, 


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CONTENTS  OF  VOL.  XLVIII. 

(FOURTH  SERIES.) 


NUMBER  CCCXV.— JULY  1874. 

P«ge 

Prof.  R.  Oausius  on  different  Forms  of  the  Virial 1 

Mr.  F.  P.  Purvis  on  Amsler's  Planimeter    11 

Prof.  A.  W.  Wright  on  the  Polarization  of  the  Zodiacal  Light,     13 
Baron  N.  Schilling  on  the  Constant  Currents  in  the  Air  and 

in  the  Sea :  an  Attempt  to  refer  them  to  a  common  Cause . .  21 
Mr.  R.  Mallet  on  the  Tidal  Retardation  of  the  Earth's  Rotation.  88 
Mr.  E.  W.  Hilgard  on  some  points  in  Mallet's  Theory  of  Vul- 

canidtir 41 

Mr.  J.  W .  L.  Glaisher  on  a  New  Formula  in  Definite  Litegrals.     53 
Dr.  J.  Rae  on  some  Physical  Properties  of  Ice ;  on  the  Trans- 
position of  Boulders  from  below  to  above  the  Ice;  and  on 

Mammoth-remains    ...    '. 56 

Mr.  P.  Clowes  on  a  Glass  Cell  with  Parallel  Sides 61 

Notices  respecting  New  Books : — 

Mr.  T.  M.  Goodeve's  Prindples  of  Mechanics    62 

The  Rev.  S.  J.  Johnson  on  Eclipses  Past  and  Future,  with 

General  Hints  for  Observing  the  Heavens 64 

Proceedings  of  the  Royal  Society : — 

Mr.  W.  Crookes  on  the  Action  of  Heat  on  Gravitating 

Masses    65 

Mr.  G.  Gore  on  Electrotorsion 70 

Proceedings  of  the  Geological  Society : — 

His  Grace  the  Duke  of  Argyll  on*  Six  Lake-basins  in 

ArgyUshire 72 

Prof.  R.  Owen  on  the  Skull  of  a  dentigerous  Bird 73 

Mr.  J.  W.  Hulke  on  the  Anatomy  of  Hypsilophodon  Foxii.     74 
Mr.  J.  Geikie  on  the  Glacial  Phenomena  of  the  '*  Long 

Isknd" 74 

Mr.  J.  F.  Campbell  on  the  Glacial  Phenomena  of  the 

Hebrides 75 

Prof.  P.  M.  Duncan  on  Fossil  Corals  from  the  Eocene 

Formation  of  the  West  Indies 76 

Mr.  R.  Etheridge  on  the  Lignite-deposit  of  Lal-Lal,  Vic- 
toria, Australia 76 

On  the  Flow  of  Saline  Solutions  through  Capillary  Tubes,  by 

Theodore  Hiibener     77 

On  Melde's  Experiment,  by  W.  Lowery     78 

On  Constant  Electric  Currents,  by  M.  Heine,  of  Halle  .....     79 
On  the  Nature  of  the  Action  of  Light  upon  Silver  Bromide, 
by  M.  Carey  Lea,  Philadelphia     80 


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IV  CONTENTS  OF  VOL.  XL VI II. — FOURTH  SERIES. 


NUMBEE  CCCXVI.— AUGUST. 

Page 
Mr.  W.  Crookes  on  Attraction  and  Eepulsion  accompanying 

Eadiation.     (With  a  Plate.)     81 

Mr.  J.  O'Kinealy  on  Fourier's  Theorem 96 

Baron  N.  Schilling  on  the  Constant  Currents  in  the  Air  and 

in  the  Sea  :  an  Attempt  to  refer  them  to  a  common  Cause    97 
Prof.  M'Leod  on  an  Apparatus  for  the  Measurement  of  Low 

Pressures  of  Ghw    110 

Dr.  W.  H.  Stone  on  Wind-pressure  in  the  Human  Lungs  du- 
ring Performance  on  Wind  Listruments     113 

Dr.  W.  H.  Stone  on  the  Fall  in  Pitch  of  Strained  Wires 

through  which  a  Ghdvanic  Current  is  passing 115 

Mr.  H.  G.  Madan  on  an  Improvement  in  the  Construction 

of  the  Spectroscope    116 

Mr.  L.  Schwendler  on  the  General  Theory  of  Duplex  Tele- 
graphy       117 

Dr.  W .  H.  Stone  on  a  simple  Arrangement  by  which  the  Co- 
loured Eings  of  Uniaxial  and  BiaxuJ  Crystals  may  be  shown 

in  a  common  Microscope 138 

Prof.  W.  F.  Barrett  on  the  Modification  of  the  usual  Trombone 
Apparatus  for  showing  the  Literference  of  Sound-bearing 

Waves 139 

Notices  respecting  New  Books : — 

M.  J.  Plateau's  Statique  Exp^rimeutale  et  Theorique  des 

Liquides  sounus  aux  seuleis  Forces  Mol^culaires 140 

Mr.  W.  B.  Birt's  Contributions  to  Selenography    141 

Proceedings  of  the  Boyal  Society : — 

Dr.  A.  C.  Bamsay  on  the  Comparative  Value  of  certain 
Geological  Ages  (or  groups  of  formations)  considered 

as  items  of  Geological  Time 143 

Prof.  O.  Eeynolds  on  the  Forces  caused  by  Evaporation 

from,  and  Condensation  at,  a  Sur&ce 146 

Proceedings  of  the  Geological  Society : — 

Prof.  W.  H.  Flower  on  the  Skull  of  a  Species  of  Halithn' 

rium  from  the  Bed  Crag  of  Suffolk 163 

Mr.  H.  Woodward  on  Forms  intermediate  between  Birds 

and  Eeptiles  .,*.,.»... 154 

Mr.  J.  W.  Hulke  on  the  Astragalus  of  IguanodonManUUi; 
and  on  a  very  1r^  Saurian  Limb-bone  from  the  Kim- 

meridge  Clay  of  Weymouth,  Dorset    155 

On  a  Simple  Ocular-Spectroscope  for  Stars,  by  F.  Zollner    . .   156 
Note  on  the  Cause  of  Tides,  by  E.  J.  Chapman,  Ph.D.,  Professor 
of  Mineralogy  and  Geology  in  University  College,  Toronto.  157 

On  the  Temperature  of  the  Sun,  by  J.  Violle     158 

On  a  Peculiar  Phenomenon  in  the  Path  of  the  Electric  Spark, 
by  Prof.  Toepler,  of  Graz 160 


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CO!9TBNTS  OF  VOL.  XLVIII. — FOURTH  SERIES.  V 

NUMBEE  CCCXVU.— SEPTEMBEE. 

Page 
Captain  Abney  on  the  Opacity  of  the  Developed  Photographic 

Image 161 

Mr.  C.  Homer  on  the  Behaviour  of  certain  Fluorescent  Bodies 

in  Castor-oil 165 

Baron  N.  Schilling  on  the  Constant  Currents  in  the  Air  and 

in  the  Sea :  an  Attempt  to  refer  them  to  a  common  Cause.  166 
Prof.  Challis  on  the  Hydrodynamical  Theory  of  the  Action 

of  a  Ghilvanic  Coil  on  an  external  small  Magnet. — Part  I. . .   180 
Prof.  A.  Stoletow  on  the  Magnetization-Eunctions  of  various 

Iron  Bodies    200 

Mr.  A,  Tylor  on  Tides  and  Waves.— Deflection  Theory.  (With 

Three  Plates.) 204 

Proceedings  of  the  Boyal  Society : — 

Mr.  H.  E.  Boscoe  on  a  Self-recording  Method  of  Measu- 
ring the  Intensity  of  the  Chemical  Action  of  Total  Day- 
light      220 

Mr.  J.  Cottrell  on  the  Division  of  a  Sound- Wave  by  a 
Layer  of  Flame  or  heated  Gas  into  a  reflected  and  a  trans- 
mitted Wave 222 

Mr.  A.  E.  Donkin  on  an  Instrument  for  the  Composition 

of  two  Harmonic  Curves ' 223 

Proceedings  of  the  Geological  Society : — 

Mr.  J.  W.  Hulke  on   the  Anatomy  of  Hypsilophodon 

Foxii 227 

Mr.  T.  Mellard  Eeade  on  the  Drift-beds  of  the  North- 
west of  England    227 

Mr.  E.  D.  Darbishire  on  a  deposit  of  Middle  Pleistocene 

Gravel  near  Leyland,  Lancashire     228 

Mr.  H.  G.  Fordham  on  the  Structure  sometimes  deve- 
loped in  Chalk    228 

Mr.  £.  Pinchin  on  the  Geology  of  the  Eastern  Province 

of  the  Colony  of  the  Cape  of  Good  Hope    229 

Lieut.  A.  W.  Stiffe  on  the  Mud-craters  and  geological 

structure  of  the  Mekran  Coast    230 

On  the  light  reflected  by  Permanganate  of  Potassium,  by 

Dr.  Eilhard  Wiedemann  231 

On  the  Temperature  of  the  Sun,  by  M.  J.  Violle  233 

Physics  of  the  Internal  Earth,  by  D.  Vaughan,  Esq.      237 

On  the  Conversion  of  Ordinary  into  Amorphous  Phosphorus 
by  the  Action  of  Electricity      239 


NUMBEE  CCCXVIU.— OCTOBEE. 

Dr.  E.  J.  Mills  on  Gladstone's  Experiments  relating  to  Che- 
mical Mass 241 

Dr.  E.  W.  Davy  on  a  very  singubr  Sulphuretted  Nitrogenous 


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VI  CONTENTS  OP  VOL.  XLVIII.— FOURTH  SBRIIt. 

Pace 
Compound,  obtained  by  the  Action  of  Sulphide  of  Ammo- 
nium on  the  Hydrate  of  Chloral 247 

Dr.  A.  Schuster  on  Unilateral  Conductivity    251 

Lord  Bayleigh  on  the  Vibrations  of  Approximately  Simple 

Systems 258 

The  late  W.  S.  Davis  on  a  simple  Method  of  Illustrating  the 
chief   Phenomena  of   Wave-motion  by  means  of  Flexible 

Cords.    (With  a  Plate.)    . . , 262 

Prof.  A.  M.  Mayer's  Eesearches  in  Acoustics. — Xo.  V 266 

Prof.  J.  J.  Miiller  on  a  Mechanical  Principle  resulting  from 

Hamilton's  Theory  of  Motion   274 

Mr.  J.  O'Kinealy  on  a  New  Formula  in  Definite  Integrals   . .   295 

Mr.  F.  Guthrie  on  an  Absolute  Galvanometer    296 

Notices  respecting  New  Books : — 

The  Eev.  J.  F.  Twisden's  First  Lessons  in  Theoretical 

Mechanics 298 

Mr.  E.  Butler  s  Supplement  to  the  First  Book  of  Euclid's 

Elements       300 

Mr.  F.  Cuthbertson's  Euclidian  Geometry 300 

Proceedings  of  the  Boyal  Society : — 

Mr.  J.  H.  N.  Hennessey  on  Displacement  of  the  Solar  Spec- 
trum   303 

Mr.  J.  H.  N.  Hennessey  on  White  liines  in  the  Sdair 

Spectrum 305 

Messrs.  Negretti  and  Zambra  on  a  New  Deep-sea  Ther- 
mometer      306 

Proceedings  of  the  Geological  Society : — 

Mr.  A.  B.  Wynne  on  the  Physical  Geology  of  the  Outer 

Himalayan  region  of  the  Upper  Punj&b,  India 310 

Mr.  E.  J.  Dunn  on  the  mode  of  occurrence  of  Diamonds 

in  South  Africa 311 

Mr.  J.  C.  Ward  on  the  Origin  of  some  of  the  Lake-basins 

of  Cumberland   311 

Mr.  D.  Mackintosh  on  the  Traces  of  a  Great  Ice-sheet  in 
the  Southern  part  of  the  Lake-district  and  in  North 

Wales 313 

Mr.  A.  W.  Edgell  on  some  Lamellibranchs  from  the  Bud- 

leigh-Salterton  Pebbles 313 

On  the  Action  of  two  Elements  of  a  Current,  by  J*  Bertrand.  314 

On  Earth-currents,  by  L.  Schwendler,  Esq 315 

Experiments  on  the  Dissipation  of  Electricity  by  Flames,  bv 

J.  W.  Fewkes    \  319 

On  the  Stratification  of  the  Electric  Light,  by  M.  Neyreneuf  .  320 


NUMBEE  CCCXIX.— NOVEMBEE. 

Mr.  H.  A .  Rowland  on  the  Magnetic  Permeability  and  Maxi- 
mum of  Magnetism  of  Nickel  and  Cobalt    321 


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CONTENTS  OP  VOL.  XL VIII. — FOURTH  8BRIB8.  VU 

PtfC 

Dr.  A.  Schuster's  Experiments  on  Electrical  Vibrations    ....  340 
Prof.  ChaUis  on  the  Hydrodynamical  Theory  of  the  Action  of 

a  Gkdvanic  Coil  on  an  External  Small  Magnet. — Part  U. . .  350 
Sir  W.  Thomson  on  the  Perturbations  of  the  Compass  pro- 
duced bj  the  rolling  of  the  Ship 363 

Br.  W.  M.  Watts  on  the  Spectrum  of  Carbon  369 

Prof.  A.  M.  Mayer's  Besearches  in  Acoustics. — No.  V 371 

Mr.  C.  Tomlinson  on  the  Action  of  Solids  and  of  Friction  in 

liberating  G^  &om  Solution    385 

Prof.  O.  Eeynolds  on  the  Surfiice-Forces  caused  by  the  Com- 
munication of  Heat 389 

Proceedings  of  the  Boyal  Society : — 

Mr.  W.  N.  Hartley  on  the  Chemical  Constitution  of  Saline 

Solutions    391 

Mr.  G.  Gore  <hi  the  Attraction  of  Magnets  and  Electric 

Conductors      393 

On  the  Temperature  of  the  Sun,  by  J.  Violle 395 

Preliminary  Notice  on  a  new  Method  for  Measunng  the  Specific 

Heat  of  Gases,  by  Eilhard  Wiedemann 398 

On  a  new  Formula  in  Definite  Integrals,  by  J.  W.  L.  Glaisher.  400 


NUMBEE  CCCXX.— DECEMBEE. 

Dr.  C.  B.  A.  Wright  on  the  Relations  between  Affinity  and 
the  Condensed  Sjrmbolic  Expressions  of  Chemical  Facts  and 

Changes  known  as  Dissected  (Structural)  FormulaB  401 

Prof.  Challis  on  the  Hydrodynamical  Theory  of  the  Action  of 
a  Gblyanic  Coil  on  an  external  small  Magnet. — Part  III. . .   430 

Prof.  A.  M.  Mayer's  Besearches  in  Acoustics. — No.  V 445 

Lord  Bayleigh  on  a  Statical  Theorem 452 

Dr.  W.  M.  Watts  on  Carbon-Spectra 456 

Mr.  J.  W.  L.  Glaisher  on  the  Problem  of  the  Eight  Queens . .  457 
Notices  respecting  New  Books  : — 

The   Hon.  Sir  W.  E.  Grove's  Correlation  of  Physical 

Forces    467 

Mr.  W.  G.  WiUson's  Elementary  Dynamics 471 

Proceeduigs  of  the  Eoyal  Society  : — 

Dr.  W.  Huggins  on  the  Motions  of  some  of  the  Nebul© 

towards  or  from  the  Earth  471 

On  the  Intensity  of  the  Light  reflected  from  Glass,  by  Dr.  P. 

Glan 475 

Pohurization  of  the  Plates  of  Condensers,  by  A.  S.  Thayer    . .   478 
On  Electrical  Currents  accompanying  the  non-simultaneous 
Immersion  of  two  Mercury  Electrodes  in  various  Liquids, 
by  G.  Quincke 479 


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VIll  CONTENTS  OF  VOL.  XLVIII. — FOURTH  SERIES. 

NUMBER  CXX^XXI.— SUPPLEMENT. 

Ptge 

M.  H.  Herwig :  the  Heat-conducting  Power  of  Mercury  in- 
dependent of  the  Temperature    481 

Prof.  J.  Lovering  on  the  Mathematical  and   Philosophical 

State  of  the  Physical  Sciences 493 

Mr.  B.  H.  M.  Bosanquet  on  Temperament,  or  the  Division 

of  the  Octave    507 

Mr.  S,  Sharpe  on  Comets  and  their  Tails    512 

Prof.  A.  M.  Mayer  s  Researches  in  Acoustics. — No.  V 513 

Mr.  F.  Guthrie  on  an  Absolute  Galvanometer  526 

Notices  respecting  New  Books : — 

Mr.  D.  D.  Heath's  Elementary  Exposition  of  the  Doc- 
trine of  Energy 527 

Mr.  B.  A.  Proctor's  Transits  of  Venus    529 

Dr.  W.  Huggins's  Approaching  Transit  of  Venus 529 

Proceedings  of  the  Boyal  Society : — 

Prof.  O.  Beynolds  on  the  Befraction  of  Sound  by  the 

Atmosphere  530 

Mr.  T.  Grubb  on  the  Improvement  of  the  Spectroscope.    532 
Drs.  Stewart  and  Schuster's  Preliminary  Experiments  on 

a  Magnetized  Copper  Wire 535 

Proceedings  of  the  G^ologicil  Society : — ' 

Mr.  J.  W.  Judd  on  the  Secondary  Bocks  of  Scotland   . .   541 
Mr.  A.  W.  Waters  on  Possils  from  Oberburg,  Styria    . .  545 
On  the  Cosmic  Dust  which  falls  on  the  Surface  of  the  Earth 

with  the  Atmospheric  Precipitation,  by  A.  E.  Nordenskiold.  546 
On  the  Passage  of  Gases  through  Liquid  Films,  by  Dr.  F. 
Exner 547 

Index 548 


ERRATUM. 
Page  203,  note  f",  line  ^A^for  liniiteil  r*ff<iiClo»ed. 


PLATES. 

L  lUuatratiTe  of  Mr.  W.  Crookes's  Paper  on  Attraction  and  Repulsion 
accompanving  Radiation. 

II..  III.,  and  iV.  Illustrative  of  Mr.  A.  Tylor's  Paper  on  Tides  and  Waves. 

V.  Illustrative  of  Mr.  W.  S.  Davis's  Paper  on  a  simple  Method  of  Illus- 
trating the  chief  Phenomena  of  Wave-motion  by  means  of 
Flexible  Cords. 


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THE 
LONDON,  EDINBURGH,  and  DUBLIN 

PHILOSOPHICAL    MAGAZINE 

AND 

JOURNAL   OF   SCIENCE. 


[FOURTH   SERIES.] 


JULY  1874. 


I.  On  different  Forms  of  the  Virial.     By  R.  Clausius*. 

MY  theorem  of  the  virial  has  already  given  rise  to  some 
discussions  on  the  forms  which  the  virial  can  assume. 
I  myself,  in  my  first  memoir  relative  to  itfi  indicated  that  when 
the  movable  points  partly  exert  forces  upon  one  another,  and 
partly  are  acted  on  by  forces  from  without,  the  virial  can  be 
analyzed  into  an  internal  and  an  external,  and  gave  their  forms 
for  certain  frequently  occurring  cases.  Yvon  Villarceau  subse- 
quently  [Comptes  Rendus,  vol.  Ixxv.)  effected  other  transforma- 
tions of  the  equation  relating  to  it,  especially  by  resolving  the 
total  motion  of  the  system  of  material  points  into  the  motion  of 
the  centre  of  gravity  and  the  relative  motions  of  the  individual 
points  about  the  centre  of  gravity,  and  referring  the  equation  to 
each  of  these  two  constituents  singly.  Prompted  by  this,  in  a 
note  published  in  the  same  volume  of  the  Comptes  Rendus  I 
added  a  series  of  further  transformations.  As,  however,  in  that 
brief  note  results  only,  without  demonstrations,  could  be  com- 
municated, and  those  but  imperfectly,  a  more  connected  treat- 
ment of  a  subject  so  important  in  itself  will  not  be  void  of 
interest. 

1.  The  simplest  form  of  the  equation  in  question  is  the  fol- 
lowing.  If  m  denotes  the  mass  of  a  material  point  which  is  in 
stationary  motion  together  with  other  material  points,  of,  y,  z 
its  rectangular  coordinates  at  the  time  /,  and  X,  Y,  Z  the  com- 

*  Tianslated  from  a  separate  impression,  communicated  by  the  Author, 
from  PoggendorflTs  Annalen,  Jubelband,  p.  41 1. 

t  Bertchie  der  Niederrhein.  Gesellsch.  fur  Natur-  u.  Heilkunde,  June 
1870;  Phil  Mag.  S.  4.  vol.  xl.  p.  122 ;  Pogg.  Ann.  vol.  cxli.  p.  124. 

PhiL  Mag.  S.  4.  Vol.  48.  No.  315.  July  1874.  B 


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2  Prof,  R.  Clau8iu8  on  different  Forms  of  the  ViriaL 

ponents  of  the  force  acting  upon  it^  then 

or,  if  (as  will  always  be  done  in  the  following)  the  first  differen- 
tial coeflScient  according  to  time  be  indicated  by  affixing  an 
accent^ 

-;r«=:-^X^+5-^ (1«) 

From  this  results,  indicating  mean  values  by  drawing  a  hori- 
zontal stroke  above : — 

'^¥'=-\y^x (2) 

If  we  name  the  quantity  ^  a^^  the  vis  viva  with  respect  to  the 

^-direction,  and  the  quantity  ""  5  ^  ^^^  virial  relative  to  the 

a?-direction,  since  the  x-  is  any  direction  we  please,  the  meaning 
of  the  equation  can  be  expressed  thus : — For  each  freely  movable 
point f  the  mean  vis  viva  relative  to  any  direction  is  eqital  the  virial 
relative  to  the  same  direction. 

If  we  form  for  a  point  the  equations  relative  to  the  three  di- 
rections of  its  coordinates  and  add  them  up,  we  get  (r  denotin<^ 
the  velocity  of  the  point,  and  /  its  distance  from  tlie  origin  of 
the  coordinates): — 

J.--|(Xx  +  yy  +  Z.)  +  ^^P.     ...    (3) 

If,  further,  we  denote  by  L  the  component,  in  the  direction 
of  /,  of  the  force  acting  on  the  point,  and  i*eckon  it  positive  fi-om 
the  origin  of  the  coordinates  onward,  the  equation  (as  is  readily 
seen)  becomes: — 

2*'=2^'+4-rfl* (*) 

It  is  obvious  that  these  equations,  which  are  valid  for  each 
individual  point,  can  be  extended  by  simple  summation  to  the 
entire  system  of  points.    We  thus  obtain : — 

-.  m  «      1  -.,  ,      1  d^XmP 

2.jr»=22L/+^-^^-5- (7) 


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Prof.  R.  Clausius  on  different  Forms  of  the  ViriaL  3 

In  the  formation  of  the  mean  values,  in  all  these  equations 
just  as  in  (1),  the  last  term  on  the  right-hand  side  falls  away ; 
and  the  expression  then  remaining  on  that  side  represents  the 
virial. 

2.  The  first  method  of  transformation  of  these  equations  is 
based  on  the  fact  that  when  the  points  are  acted  on  by  forces  of 
different  sorts  which  we  wish  to  consider  singly,  the  force-com- 
ponents can  be  separated  into  as  many  summanda  as  the  kinds 
of  force  that  are  to  be  distinguished,  whereby  the  virial  is  divided 
into  just  as  many  parts. 

If,  for  instance,  the  above-mentioned  distinction  be  made  be- 
tween the  forces  which  the  points  of  the  system  exert  on  each 
other,  and  those  which  act  upon  the  system  from  without,  and 
this  be  denoted  by  the  indices  i  and  e,  we  can  put  X  =  X,  -f  X^; 
and  the  same  holds  for  the  components  Y,  Z,  and  L.  It  is 
readily  seen  how  the  above  equations  are  changed  by  the  inser- 
tion of  these  sums.  Equation  (6),  for  example,  thereby  changes 
into 

^is?- ^^) 

When  more  special  assumptions  are  made  concerning  the 
nature  of  the  forces,  the  expressions  also  take  more  special  forms, 
of  which  I  will  briefly  cite  two  which  are  exhibited  in  my  first 
memoir.  When,  namely,  the  internal  forces  consist  of  reciprocal 
attractions  or  repulsions^  which,  according  to  any  law,  depend 
on  the  distance,  so  that  for  two  points  whose  distance  is  r  the 
force  (which  as  an  attraction  is  reckoned  positive,  and  as  a  repul- 
sion negative)  can  be  represented  by  a  function  ^(r),  we  can  put 

-\l.{7.f  +  Y,y^Z,z)  =  \lr<i>{r),       ...     (9) 

in  which  the  sum  on  the  right-hand  side  refers  to  all  combina- 
tions of  two  mass-points  each.  When  the  system  of  points  is 
further  considered  as  a  body  on  which  the  only  external  force 
acting  is  a  symmetrical  pressure/?  normal  to  the  surface,  we  can  put 

-|2(X,^+Y,y  +  Z,r)=|pV.     ....     (10) 

in  which  V  denotes  the  volume  of  the  body. 

3.  Another  mode  of  transformation  depends  on  the  separation 
of  the  coordinates  of  the  points  into  summanda. 

To  this  belongs  the  transformation  effected  by  Yvon  Villar- 
ceau.     If,  namely,  besides  the  fixed  systems  of  coordinates,  we 

B2 


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4  Prof.  R.  Clausius  on  different  Forms  of  the  Virial. 

introduce  a  movable  system  having  for  its  origin  the  centre  of 
gravity  of  all  the  material  points^  and  parallel  to  the  fixed  sy stem, 
and  if  we  name  the  coordinates  of  the  centre  of  gravity  in  rela- 
tion to  the  fixed  system  Xc,  y^  ^o  ^^^  the  coordinates  of  any  one 
of  the  material  points  in  relation  to  the  movable  system  ^,  77,  ^, 
then  is 

^=^c+f,     y-Vc^Vy    ^='8'r+(; 
If  we  now  form  the  equation 

and  consider  that  we  may  put 

we  gct^  if  M  denotes  the  total  mass  of  all  the  material  points^ 
consequently  the  sum  Sm,  the  equation 

2wa^=Ma:J  +  2wf« (11) 

In  precisely  the  same  manner  we  obtain 

2W*=M;r'J  +  27n^« (12) 

Finally,  the  mere  substitution  in  SXj?  of  a?^  +  f  for  the  coor- 
dinate X,  Xp  denoting  the  sum  2X,  gives 

2Xa-  =  X,^e  +  2Xf (13) 

If  now  we  form  for  the  centre  of  gravity  the  identical  equation 
which  for  a  single  material  point  has  served  for  the  derivation 
of  (1),  viz. 


2    <//«     ~\dt)  '^'''  dt*' 


which,  after  multiplication  by  ^,canbe  writtcD  thu.4. 


and  suppose  herein 

3 
we  then  obtain 


**  rf?^^'"5?''^^^^" 


2^'-   2^*'+  4^r« (^*) 

With  the  aid  of  this  equation  in  conjunction  with  (11),  (12), 
and  (13),  the  following  equation  can  be  immediately  derivtd  from 

(5):- 


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Prof.  R.  Clausios  on  different  Forms  of  the  VirtaL         5 

2^r»=-^2Xf+l^.      .    .    .     (15) 

All  the  equations  above  derived  for  the  j?-direction,  of  course 
bold  good  in  a  corresponding  manner  for  the  other  two  direc* 
tions  of  coordinates ;  and  when  each  three  equations  thereby 
arising  are  added  together^  a  new  system  of  equations  is  ob- 
tained. In  order  to  write  these  conveniently^  let  us  introduce 
the  following  symbols.  We  will  nanie  the  distance  of  the  centre 
of  gravity  from  the  origin  of  the  fixed  coordinates  /<.;  and  the 
distance  of  a  mass-point  from  the  centre  of  gravity,  \.  Let  the 
velocity  of  the  centre  of  gravity  be  called  Vc,  and  the  relative 
velocity  of  a  mass-point  about  the  centre  of  gravity,  consequently 
the  quantity  \/f  4-»/*+|^*,  be  called  w.  Further,  of  the  force 
whose  components  in  the  coordinate-directions  are  X^,  Yc,  Z<., 
the  component  in  the  direction  of  /«  may  be  denoted  by  17^ ;  and 
of  the  force  acting  on  a  mass-point,  let  the  component  in  the 
direction  of  X  be  denoted  by  A.  Then  the  equations  will  be 
written  as  follows : — 

2w/«=M/J-f-2mX«, (16) 

ltnv^=Mvl  +  l.mw^, (17) 

2L/=LA-h2xV\, (18) 

*^.«     Iri^^^i^)  119) 

^t.,=  ^LA+4   ^^.       ....     (19) 

2fu;'=l2AX+^^'|p^'.     •.     .     .     (20) 

4.  We  will  now  turn  to  the  kind  of  transformation  which  I 
communicated  in  the  Comptes  Rendus,  and  which  depends  on  the 
introduction  into  the  formulee  of  the  mutual  distances  and  rela- 
tive velocities  of  each  two  material  points. 

Firsts  if  V  and  fi  represent  any  two  of  the  indices  1,  2, 3,  &c., 
and  accordingly  m^  and  m^  are  any  two  of  the  given  mass-points 
with  the  coordinates  Xy,  yy,  Zy  and  ^^  y^,  z^^y  we  can  form,  corre- 
sponding to  the  above,  the  following  identical  equation, 

or,  differently  arranged  and  written. 


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6  Prof.  R.  Clausius  on  different  Forms  of  the  ViriaL 

which  by  introducing  the  force-components  is  changed  into 

Just  such  equations  hold  for  the  other  two  coordinate-directions ; 
and  we  will  add  up  these  three  equations.  Therein  the  distance 
between  the  two  points  shall  be  denoted  by  r ;  and  their  relative 
velocities,  consequently  the  quantity 

we  will  call  u.  Lastly,  of  the  forces  acting  on  the  mass-points 
m^  and  m^,  let  the  components  which  fall  in  the  direction  of  r 
be  denoted  by  B^  and  R^,  and  at  the  same  time  let  the  direction 
of  force  from  each  point  to  the  other  point  be  reckoned  positive. 
We  can  then  put : — 

Xy{x^—Xy)  +Y^(y^— y^)  +Z^(j2r^-5r^)  =  R^, 

X^(^,,-4?^)  +  Y^yr-y^)  +  Z^(j8r,--r^)=R^r. 

Accordingly  the  equation  resulting  from  the  above-mentioned 
addition  takes  the  following  form  : — 

Into  this  we  will  introduce  another  simpUfying  symbol,  putting 

the  equation  will  then  read  : — 

„.=a,+^) (24) 

Multiplying  this  equation  by  ^—^  and  extending  it  to  the 
entire  system  of  points,  wc  get 

A2«^^„«=_l-2m^^»,+  _l.^^',  .    (2J) 

wherein  the  three  sums  refer  to  all  the  combinations  of  two  each 
of  the  given  mass-points. 

5.  Between  the  sums  which  occur  in  this  equation  and  the 
sums  previously  considered,  there  are  simple  relations,  which 
can  be  discovered  by  means  of  a  general  formula  of  transforma- 
tion. For,  besides  the  masses  tw,,  7n^  . . .  m„,  given  two  other 
groups  of  quantities  belonging  to  them,  which  shall  provisionally 


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Prof.  R.  Clausios  on  different  Farms  of  the  ViiioL         7 

be  denoted  hj p^,p^  .../>«  and  jj,  y^, . . .  j«,  then  the  following 
identical  equation  holds : — 

2m^^(/?^--/?^)(gf^— gr^)=2m2inpj— SmpSmj;     .     .     (26) 

in  which  the  sum  on  the  left-hand  side  refers  to  all  combinations 
of  two  masses  each^  while  the  sums  on  the  right-hand  simply  refer 
to  all  the  masses.  A  conviction  of  the  correctness  of  the  equation 
can  be  obtained  by  carrying  out  the  multiplication  on  the  left- 
hand  side^  and  suitably  arranging  and  collecting  the  terms  then 
contained  in  the  sum.  We  will  now  apply  this  equation  to  our 
case  by  attributing  successively  different  significations  to  the 
quantities  p  and  q. 

First  let  ua  prxtp^q^x;  the  result  is: — 

Xm^f^{x^^x^^='ZmS,ma^'-  (2i?wr)*=M2mar'— M*a?J. 
We  then  fxitp=q=a^,  and  obtain  in  a  corresponding  manner 
2f7i^^(a/,  -a^^)«=M2ma/«-.M«a?';. 

Lastly,  we  put  /;=  —  and  q^x;  then  comes 

2m,»i^(~  -  ^-^)(a?,-ar^)=2m2Xa?-2X2in^ 

=M2X5?-MXcare. 

Just  such  equations  are  valid  for  the  other  two  directions  of 
coordinates ;  and  if  we  form  the  sum  of  each  three  belonging  to 
one  another  and  divide  it  by  M,  we  obtain  the  equations  ex- 
pressing the  relations  sought,  namely : — 

j^2m,7n^r«=2m/«-M/2,        ....     (27) 
^2m,7n^u«=2mt^-MrJ,       ....     (28) 

^2^^»r=2L/-Le/e (29) 

Combining  these  with  equations  (16),  (17),  and  (18),  we  get 
the  following  very  simple  equations : — 

^2m,m^r«  =  2»«\«, (80) 

jg-2m^^tt'=2mi(;*, (31) 

^2m,m^»r=2A\ (82) 


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8  Prof.  R.  Clausius  on  different  Farms  of  the  Firiat. 

It  scarcely  needs  to  be  meotioDed  that  in  equations  (8),  (14), 
(15),  (19),  (20)^  and  (25)^  as  well  as  in  the  earlier  corresponding 
equations,  with  the  formation  of  mean  values  the  last  term 
(which  is  a  differential  coefficient  according  to  time)  drops  out, 
and  the  terms  then  remaining  on  the  right-hand  side  are  forms 
for  virials,  the  special  signification  of  which  is  readily  seen  in  the 
individual  cases. 

6.  Having  thus  far  been  occupied  in  introducing  special  quan- 
tities of  various  kinds  for  the  determination  of  the  virial^  we  will 
finally  derive  some  equations  which,  in  relation  to  the  variables 
to  be  employed,  are  perfectly  general. 

Given  any  variables  serving  to  determine  the  positions  of  the 
points,  and  denoted  by  q^,  q^  q^  &c.,  then  the  coordinates  of 
the  points,  and  all  the  quantities  determined  by  them,  are  to  be 
regarded  as  functions  of  these  general  variables.  The  velocities, 
and  the  quantities  determined  by  them,  can  accordingly  be  re- 
presented as  functions  of  these  variables  and  of  their  coefficients 
of  differentials  according  to  time.  Let  us  now  assume  that  the 
forces  acting  in  our  system  have  a  force-function  or  ergal  U,  we 
can  treat  this  as  a  function  oi  q^,  q^^  q^  &c.,  and  at  the  same 
time  the  vis  viva  T  of  the  system  as  a  function  of  ^„  q^  q^  &<;. 
and  ^,,  9',,  q'of  &c.  Between  these  two  functions  there  subsists, 
according  to  Lagrange,  the  following  equation, 

in  which  the  sum  refers  to  the  variations  of  all  the  variables 

9v  99>  9s9  &c*     If*  fo**  abbreviation,  we  introduce  the  symbols 

Pv  P2f  P9>  ^'»  ^^^  f^^ 

dT 

^    P'-W.' ^''^* 

V  signifying  any  one  of  the  indices  ^,  v  s>  ^^^  preceding  equa- 
tion  becomes : — 


SU 


=X[^-j/)Sq.       ....     (85) 

Besides,  according  to  Lagrange,  the  following  easily  derived 
equation  holds  for  the  vis  viva  T : — 

T=|2;»?' (86) 

If  wc  now  differentiate  according  to  time  the  product  p^,  q^, 
we  have 

rf(M.)  =p^,^,^qj,, 


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Prof.  R.  Clausius  on  different  Forms  of  the  ViriaL  9 

whence  results 

;'y.=  -?y,+  ^ (37) 

Herein^  (orp^,,  we  can  put  an  expression  to  be  obtained  from 
(85).  For  this  purpose  we  will  write  (35)  in  the  following 
form: — 

2f «?=2(^-p'>.    .    .    .      (88) 

If  now  the  variables  q^,  q^  q^  &c.  are  each  independent  of  the 
others^  their  variations  are  also  independent  of  each  other,  and 
the  equation  which  holds  for  the  sum  of  all  the  terms  must  also 
hold  for  each  term  singly ;  we  consequently  obtain 

dq,      dq^    ^ -^ 
or 


If  we  insert  this  expression  for  j&^  in  equation  (37),  after  mul- 
tiplying it  by  \,  we  get 

2^'^"     2      dq^      ^'^  2      dt'   '     '     •     •     ^^^> 

and  when  we  form  the  sum  of  all  the  equations  of  this  kind,  we 
obtain,  in  accordance  with  (36), 

1      rf(U-T)         \dtpq 
^"2^       dq      ^^%    dt    '      •     •     •     ^^^^ 

These  equations  (40)  and  (41)  are  two  new  equations  represent- 
ing generalizations  of  equations  (1)  and  (6). 

By  forming  the  mean  values,  new  forms  of  virial-cxpressions 
can  be  deduced  from  them.  In  the  first  place,  the  expression 
for  the  total  virial  resulting  from  the  last  equation  is : — 

2^       dq       *+2'^r" 

In  regard  to  the  last  term  in  this  expression  a  special  remark 
must  be  made.  ITie  variables  q.^  q^,  S's  >  •  •  •  s^^^ve  for  the  deter- 
mination of  the  positions  of  the  movable  points;  and,  con- 
versely, the  values  of  the  variables  can  be  determined  from  the 
positions  of  the  points.  This  latter  determination,  however, 
may  take  place  in  two  ways.  It  may  have  but  one  meaning — 
which  is  the  case  for  right-line  coordinates,  the  distances  of  the 
movable  points  from  one  another  or  from  fixed  points  or  the 
centre  of  gravity,  and  for  the  trigonometrical  functions  of  the 


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10         Prof.  R.  Clausius  on  different  Farm  of  the  Virial. 

angles  made  by  such  right  lines;  or  it  may  be  ambiguaui — 
which  is  the  case  with  the  angles  themselves^  since  to  one  direc- 
tion an  infinite  number  of  angles  belongs  which  differ  from  one 
another  by  27r.  In  the  former  case  l,pq  is  a  quantity  the  value 
of  which,  with  a  stationary  motion,  varies  only  within  certain 
limits ,  and  accordingly  the  mean  value  of  the  differential  coe£S- 
cieut,  taken  according  to  time,  of  this  quantity  may  at  once  be 
regarded  as  vanishing  and  be  omitted  from  the  above  expres- 
sion. In  the  latter  case,  on  the  contrary,  the  mean  value  of  that 
differential  coe£Bcient  does  not  necessarily  vanish,  and  hence  it 
must  remain  in  the  expression  for  further  consideration. 

Should  the  variables  q^,  g^,  g^,  &c.  not  be  all  independent, 
but  connected  with  one  another  by  certain  condition-equations, 
then  we  can,  notwithstanding,  obtain  equations  similar  in  form 
to  (40)  by  employing  Lagrange's  indeterminate  coefficients. 
Let,  namely, 

&c. 

be  the  given  condition-equations,  we  form  instead  of  (38)  the 
following  equation, 

where  p,  o-,  &c.  are  indeterminate  coefficients ;  and  this  equation 
is  to  be  resolved,  in  the  usual  way,  into  as  many  partial  equa- 
tions as  there  are  variations.  The  partial  equation  correspond- 
ing to  the  variable  q^  is  then 


dV      rfT        I  ^    d4>^    dit      . 
dq^      dq,     "^"^     "^dq^        dq^ 


whence  results 


rf(T--U)        d^        rff 


(42) 


By  the  insertion  of  this  value  of  j/^  equation  (87)  is  changed 
into 

^"^^      L      dq^  ^dq^        dq^  ^^^      dt  ^     ^ 

As  many  equations  of  this  form  are  obtained  as  the  given  vari- 
ables 9„  ^9,  ^3,  &c.;  and  the  work  can  be  supplemented  by  eli- 
minating from  them  the  indeterminate  coefficients. 

It  is  thus  shown  in  a  general  way  how  the  equations  which 


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Mr.  Y.  P.  Parvis  on  Amsler's  Plardmeter.  11 

serve  for  the  determination  of  the  virial  can  be  formed  with  the 
employment  of  any  variables;  and  with  this  I  think  I  may  on 
the  present  occasion  be  satisfied^  without  entering  upon  special 
applications  of  the  equations — which  may  be  of  very  various 
kinds,  and^  hence,  would  lead  to  extended  discussions. 


II.  On  Amskr^s  Plmimeter.     By  F.  P.  Purvis,  Esq.* 

THE  following  is  a  simple  and  thoroughly  general  explana- 
tion of  the  action  of  this  perplexing  little  instrument. 
Suppose,  for  simplicity  and  greater  generality,  that  the  instru- 
ment consisted  simply  of  the  straight  bar  A  B,  of  length  /,  car- 


rying a  pencil  at  each  end,  A  and  B ;  and  suppose  any  lines  A  a, 
B  b  were  traced  out  by  these  pencils  :  we  will  consider  how  the 
area  A  a  ^  B  may  be  expressed  in  terms  of  /  and  the  motion  of 
some  point  in  the  line  AB. 

Let  the  motion  from  AB  to  ayS  represent  an  elementary 
motion  of  the  bar,  the  centre  of  it  C  moving  from  C  to  7,  and 
the  bar  turning  about  y  through  the  angle  dO ;  let  rfnaa  the 
normal  distance  from  y  to  A  B ;  this  motion  may  be  considered 
to  take  place  in  two  parts : — Ist,  the  motion  of  A  B  parallel 
to  itself  into  the  position  xy  ;  2nd,  the  motion  of  AB  about  its 
centre  into  the  position  a/S;  the  required  area  A  a  ^  B  is,  in 
this  elementary  motion,  equal  to  the  area  AxyB  {^Idn),  since 
the  area  7 a x  =  the  area  7  jS y,  and  the  areas  A  aw  and  B^y 
are  negligible  with  respect  to  Idn,  being  the  product  of  two  in- 
finitesimal quantities,  while  Idn  is  the  product  of  one  infinitesi- 
mal quantity  (comparable  with  each  of  the  two  just  mentioned) 
and  the  finite  quantity  /. 

Integrating  for  the  whole  area  A  a  &  B,  we  see  that  it  is  ex- 
pressed by  In,  where  n  is  the  travel  of  the  point  C  normally  to 
the  bar  A  B. 

Now  we  may  obtain  that  normal  motion  n  by  centring  a 
wheel  on  the  bar  at  C,  free  to  revolve  in  the  plane  at  right  angles 

*  Communicated  bv  the  Author. 


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12 


Mr.  r.  P.  Purvis  on  Amsler's  Planimeter. 


to  A  B^  and  resting  at  its  circumference  on  the  paper.  That  it  is 
given  by  the  circumferential  motion  of  this  wheel  may  be  seen 
by  considering  again  the  elementary  motion  of  the  bar  from  A  B 
to  «  ^ :  while  the  bar  moves  from  AB  to  ar  j^,  the  wheel  turns 
through  the  normal  distance  from  7  to  AB;  while  the  bar 
turns  about  the  point  y,  the  wheel  remains  stationary. 

If  instead  of  centring  the  wheel  at  C  we  centre  it  at  any 
other  point  J),  distant  m  from  C,  its  circumferential  travel  for 
the  elementary  motion  will  be  the  normal  from  z  to  A  B(  =  dn) 
--mdO,  and  for  the  whole  motion  from  A  B  to  a  ^  will  be  n-^mO, 
where  ^=  the  inclination  of  a  &  to  A  B. 

If  a  retrograde  motion  be  now  given  to  the  instrument,  bring- 
ing it  into  the  position  c/b',  the  product  nl  will  still  equal  the 


area  included  between  AaJ^Bb  b\  and  the  two  straight  lines 
A  B  and  Jlf,  part  of  that  area  being,  in  the  case  shown,  negative ; 
nl=iAaa!  IB-^lbb^  If  instead  of  allowing  B  to  take  any  path 
bV  ift  constrain  it  to  move  only  along  the  line  already  traced, 
while  A  traces  out  a  new  line  a  a,  the  negative  area  will  be  nil, 


and  the  product  nl  will  equal  the  area  Aaalb^B,  If  this  motion 
be  continued,  B  being  always  kept  in  the  path  A^B  until  AB 
occupies  its  initial  position,  the  product  nl  will  equal  the  area 
A  a  a'  A,  whatever  be  the  nature  of  the  line  Bbf  b.  Also  for  the 
whole  motion  ^=0;  so  that  the  circumferential  travel  of  the 
wheel  at  D  =  n,  entirely  independently  of  the  value  of  m. 


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On  the  Polarization  of  the  Zodiacal  Light.  1 3 

Now  in  Amsler'a  planimeter  the  point  B  is  constrained  to 
move  in  the  arc  of  a  circle,  while  the  pencil  A  is  traced  ronnd 
the  contour  of  the  required  area ;  this  is  simply  a  limitation  of 
the  more  general  case  taken  above.  Also  the  wheel  whose 
travel  is  measured  is  placed  away  from  the  centre  of  the  bar  C, 
and  indeed  on  the  opposite  side  of  B ;  but,  as  we  have  seen,  its 
position,  so  long  as  its  centre  is  oa  the  line  AB,  is  quite  imma* 
terial,  its  motion  in  the  aggregate  being  the  same  as  if  it  were 
placed  at  G. 

In  the  planimeter  the  length  /  is  capable  of  variation  ;  so  that, 
by  setting  it  differently,  the  same  graduation  on  the  wheel  will 
give  areas  in  different  units,  the  unit  of  area  being  always  Ix 
the  circumferential  travel  of  the  wheel  required  to  alter  its  read- 
ing by  unity. 


III.  On  the  Polarization  of  the  Zodiacal  Lif/ht. 
By  Professor  Arthur  W.  Wright*. 

FROM  the  published  accounts  of  observations  upon  the  zo- 
diacal light,  it  would  seem  that  few  attempts  have  as  yet 
been  made  to  determine  whether  or  not  any  portion  of  the  light 
is  polarized,  and  the  results  thus  far  obtained  leave  the  question 
still  undecided.  The  few  notices  that  can  be  found  in  the  scien- 
tific journals,  though  uncertain  and  contradictory,  tend  to  the 
view  that  it  is  either  not  polarized  at  all,  or  that  the  proportion 
of  polarized  light  is  so  small  as  to  render  its  detection  a  matter 
of  excessive  difficulty.  It  may  be  observed  that  most  of  the 
observations  giving  negative  results  appear  to  have  been  made 
with  Savart's  polariscope ;  but  with  an  instrument  which  ab- 
sorbs so  large  a  proportion  of  the  light  as  a  Savart,  the  amount 
of  polarization  necessary  to  render  the  bands  visible  increases 
very  greatly  as  the  light  becomes  fainter,  and  especially  so  as  it 
approaches  the  limit  of  visibility.  Numerous  attempts  have 
been  made  by  the  writer  to  detect  traces  of  polarization  with  a 
Savart,  but  never  with  the  slightest  result,  excepting  that  on  one 
especially  clear  evenings  when  the  zodiacal  light  was  unusually 
distinct^  the  bands  seemed  to  be  visible  by  glimpses,  on  the 
utmost  exertion  of  visual  effort.  The  observation  was  so  un- 
certain, however,  that  it  was  considered  worthless. 

Nearly  a  year  ago  a  series  of  observations  was  begun,  in  the 
course  of  which  a  variety  of  apparatus  were  employed,  by  the  use 
of  which  it  was  hoped  polarization  might  be  detected,  either,  as 
in  the  Savart,  by  bands  or  other  variations  in  the  brightness  of 
parts  of  the  field,  or  as  with  the  double-image  prism,  the  NicoPs 

*  From  Silliman's  American  Journal,  May  1874. 


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14  Prof.  A.  W.  Wright  en.  the  Polarization 

prism^  or  a  bundle  of  glass  plates  set  at  the  polarizing  angle>  by 
a  diminution  of  the  brightness  of  the  object  itself.  None  of 
them,  however,  gave  results  of  any  value.  In  resuming  the 
study  of  the  subject  some  months  later^  the  attempt  was  made 
to  find  a  combination  which  should  give  a  large  field  of  view, 
and  which,  while  absorbing  as  little  light  as  possible,  should  in- 
dicate the  pre^nce  of  even  small  proportions  of  polarized  light, 
by  sufficient  variations  of  intensity  to  render  it  available  with 
the  faintest  visible  illumination. 

A  Savart  in  which  the  tourmaline  was  replaced  by  a  Nicol, 
though  possessing  almost  perfect  transparency,  was  found  to 
give  too  small  a  field  of  view,  and  bands  too  faint  to  render  it 
of  any  service.  Amother  instrument  was  constructed  on  a  plan 
similar  to  that  adopted  by  Mr.  Uuggins  in  observations  upon 
Encke*s  comet*,  by  placing  a  large  double-image  prism  in  the 
end  of  a  tube  18  inches  long,  the  other  end  of  which  had  a 
square  aperture  a  little  more  than  an  inch  in  diameter.  The 
distance  was  so  adjusted  that  the  two  images  just  touched  with- 
out overlapping.  This  seemed  to  promise  well ;  and  on  using 
it  diflferences  of  intensity  were  perceived  which  indicated  polari* 
zation  in  a  plane  passing  through  the  sun.  Two  defects,  how- 
ever, are  inherent  to  this  mode  of  investigation  : — one,  that  if 
the  field  is  not  of  uniform  brightness  thi-oughout,  the  brighter 
side  of  one  image  may  be  juxtaposed  to  the  fainter  side  of  the 
other,  thus  giving  rise  to  false  conclusions ;  another  is  the  un- 
equal sensibility  of  diflFerent  parts  of  the  i*etina.  In  consequence 
of  this,  the  one  of  the  images  directly  viewed  seems  always  the 
more  obscure,  and  the  true  relation  of  their  intensities  can  only 
be  found  by  indirect  vision,  the  eye  being  turned  to  some  point 
in  the  median  line  of  the  images.  Although  when  used  with 
the  observance  of  the  necessary  conditions  this  instrument  is 
capable  of  ginng  trustworthy  indications,  it  was  soon  abandoned 
for  a  better. 

Among  the  polariscopic  apparatus  belonging  to  the  physical 
cabinet  of  Yale  College,  a  quartz  plate  was  found,  cut  perpendi- 
cularly to  the  axis,  and  exhibiting  by  polarized  light  an  unusual 
intensity  of  colour.  It  is  a  made,  the  body  of  the  plate  consist- 
ing of  left-handed  quartz,  through  which  passes  somewhat  ex- 
centrically  a  band  of  right-handed  quartz,  6*5  millimetres  in 
breadth.  This  band  is  not  bounded  by  sharp  lines  of  division 
on  the  sides,  but  by  intermediate  strips  {b,  o  in  the  figures), 
about  2  millimetres  in  breadth,  which  are  of  different  structure, 
and  are  apparently  formed  by  the  interleaving  of  the  strata  of 
the  two  portions  at  their  edges.  In  the  polarizing  apparatus 
these  strips  simply  vary  from  bright  to  dark,  without  marked 
♦  Phil.  Mag.  S.  4.  vol.  xliii.  p.  382. 


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of  the  Zodiacal  Light,  1 5 

appearance  of  colour.  Placed  between  two  Nicols,  the  plate  has 
the  appearance  represented  in  the  accompanying  figures^  which 
are  drawn  of  full  size.    When  the  corresponding  diagonals  of 

Fig.  1.  Fig.  2. 


the  Nicols  are  parallel,  or  nearly  so,  the  bands  are  white  upon 
a  deep  reddish- puq)le  ground,  as  shown  in  fig.  1 ;  with  the 
Nicols  crossed,  the  bands  are  dark  upon  a  light  greenish-yellow 
background,  as  represented  in  fig.  2.  Turning  one  of  the 
Nicols  45°  in  one  direction,  the  observer  sees  the  central  band 
a  intensely  blue  upon  a  yellow  ground ;  turning  in  the  other 
direction,  a  bright  yellow  upon  a  dark  blue;  and  intermediate 
positions  give  the  usual  varying  tints.  Examined  with  one  Nicol 
and  unpolarized  light  the  plate  is  perfectly  colourless,  and  shows 
no  trace  of  its  heterogeneous  structure. 

The  quartz  plate  was  placed  in  one  end  of  a  tube,  large  enough 
to  admit  its  full  size  very  nearly,  and  11  inches  in  length. 
This  was  found  better  than  a  shorter  one,  as  the  bands  are  most 
easily  seen  when  not  nearer  the  eye  than  the  limit  of  distinct 
vision.  In  the  other  end  was  placed  a  good-sized  Nicol ;  and 
the  tube  was  provided  with  a  joint,  so  that  the  latter  could  be 
easily  turned.  Thus  mounted  the  plate  and  Nicol  form  a  po- 
lariscope  of  extraordinary  sensibility,  with  faint  light  far  excel- 
ling the  best  Savart,  and  even  with  strong  light  somewhat 
superior  to  it.  The  instrument  is  especially  suited  for  the  detec- 
tion of  small  degrees  of  polarization,  and  the  examination  of 
very  faint  lights.  The  occurrence  of  the  narrow  strips  is  pecu- 
liarly advantageous,  as  with  very  feeble  illumination  they  appear 
bright  upon  a  dark  ground,  or  the  reverse,  and  are  thus  more 
easily  seen.  The  efficiency  of  the  instrument  is  further  increased 
by  the  comparatively  large  field  of  view  and  the  perfect  trans- 
parency of  the  whole  combination. 

As  a  test  of  its  delicacy  may  be  mentioned  that  when  a  glass 
plate  is  laid  upon  the  window-sill,  and  the  light  of  the  sky  in  a 
clear  moonless  night,  after  reflection  from  it,  is  viewed  through 
the  instrument,  both  bright  and  dark  bands  are  easily  seen,  the 
former  appearing  surprisingly  luminous  in  contrast  with  the 


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16  Prof.  A.  W.  Wright  on  the  Polmisalion 

darkened  field.  The  plane  of  polarization  is  easily  determined 
with  it^  since  when  the  bright  bands  appear,  as  iu  fig.  1,  the 
longer  diagonal  of  the  Nicol  is  in  that  plane ;  when  the  bands 
are  dark,  the  plane  of  polarization  is  parallel  to  the  shorter 
diagonal. 

On  the  completion  of  the  instrument  the  first  favourable  op- 
portunity was  iinproved  to  test  its  efficiency  upon  the  zodiacal 
light  it  was  almost  immediately  found  to  indicate  the  exist- 
ence of  light  polarized  in  a  plane  passing  through  the  sun. 
The  bands  were  fainter  than  had  been  expected,  and  at  first  were 
overlooked.  More  careful  attention,  however,  and  the  obser- 
vance of  suitable  precautions  established  their  presence  beyond 
a  doubt.  The  observations  were  made  in  a  room  in  the  upper 
floor  of  one  of  the  college  buildings,  the  windows  of  which  look 
toward  the  south-west,  and  command  a  clear  view  nearly  to  the 
horizon.  The  room  during  the  observations  received  light  only 
from  the  sky,  which  sufficed  to  render  objects  dimly  visible.  After 
being  exposed  only  to  this  dim  light  for  ^ih^exi  or  twenty  minutes, 
the  eye  became  sufficiently  sensitive  for  observation.  This  was 
a  very  necessary  precaution,  as  a  moment's  exposure  to  a  bright 
light  rendered  the  eye  unfit  for  delicate  discrimination  of  lumi- 
nous intensities  for  a  long  time.  The  Nicol  of  the  instrument 
was  now  turned  round  and  round,  so  that  no  previous  know- 
ledge of  its  position  relatively  to  the  bands  of  the  quartz  plate 
might  intiuence  the  judgment  as  to  their  character  and  position. 
On  looking  through  the  tube  at  the  zodiacal  light,  and  turning 
the  whole  instrument  slowly  round,  it  was  possible  to  find  a 
position  where  the  bands  could  be  seen,  and  their  nature  and 
direction  determined.  They  could  rarely  be  seen  steadily  by 
direct  vision,  and  then  only  for  a  few  moments,  as  the  excite- 
ment and  fatigue  of  the  eye  consequent  upon  the  straining 
effort  of  vision  soon  rendered  the  field  a  confused  blur.  Allow- 
ing the  eye  to  rest  a  few  minutes,  also  on  turning  it  obliquely 
and  rapidly  directing  it  to  different  parts  of  the  field,  and  espe- 
cially by  suddenly  bringing  it  to  focus  upon* the  quartz  plate, 
the  bands  could  be  distinctly  seen,  and  their  direction  fixed  with 
a  good  degree  of  certainty.  On  the  clearest  nights  the  brightest 
bands  (6,  b,  fig.  1)  were  seen  without  much  difficulty,  the  broad 
dark  band  (a),  corresponding  to  an  inclination  of  45^  in  the 
Nicol,  less  easily,  and  the  dark  bands  (6,  A,  fig.  2)  by  glimpses. 
After  determining,  by  repeated  observations,  the  angle  made  by 
each  of  the  bands  with  some  fixed  line,  as  the  axis  of  the  zodiacal 
light,  or  a  line  nearly  parallel  to  it  drawn  between  two  known 
stars,  the  position  of  the  plane  of  polarization  was  found,  by 
means  of  light  from  a  gas- flame  reflected  from  a  sheet  of  white 
paper  placed  in  a  suitable  position,  or  by  observing  the  position 


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of  the  Zodiacal  Light.  17 

of  the  Nicol.  The  resalts  of  the  numeroad  observations  of  dif- 
ferent evenings  were  entirely  concordant^  and  showed  that  the 
plane  of  polarization  pasaes  through  the  sun^  as  nearly  as  it  was 
possible  to  fix  its  direction.  In  no  instance  when  the  sky  was 
clear  enough  to  render  the  bands  visible  did  their  position^  as 
determined  by  the  observations,  fail  to  agree  with  what  would 
be  required  by  polarization  in  a  plane  through  the  sun.  Not 
the  slightest  trace  of  bands  was  ever  seen  wl^n  the  instrument 
was  directed  to  other  portions  of  the  sky. 

These  observations,  for  the  most  part,  were  made  in  the  ten 
days  preceding  new  moon  in  January  and  February  of  the  pre- 
sent year.  During  this  time  there  was  an  unusual  number  of 
clear  nights,  with  the  atmosphere  cold  and  still.  A  few  good 
evenings  in  March  and  April  also  were  improved  in  verifying 
the  results  previously  obtained.  The  absence  of  the  moon,  and 
the  distance  of  any  of  the  brighter  planets  and  stars  from  the 
field  of  observation,  removed  all  uncertainties  from  these  sources. 
As  the  instrument  was  directed  to  points  from  30  to  40  or  even 
more  degrees  from  the  sun,  the  polarization  could  not  have  pro- 
ceeded from  faint  vestiges  of  twilight.  That  it  did  not  arise  by 
reflection  of  the  zodiacal  light  itself  in  the  atmosphere,  or  from 
atmospheric  impurities,  is  shown  both  by  its  amount  and  the  fact 
that  it  was  always  most  easily  discernible  on  the  clearest  nights. 

The  next  step  was  to  determine  what  percentage  of  the  light 
is  polarized.  The  failure  of  the  common  apparatus  to  detect  it 
shows  that  the  proportiou  is  not  large ;  but  it  must  be  recollected 
that  for  a  light  so  very  faint  much  greater  differences  of  inten- 
sity are  imperceptible  than  in  cases  where  the  luminous  intensity 
is  greater.  The  determinations  were  made  as  follows.  A  bundle 
of  four  pieces  of  excellent  plate  glass  was  placed  vertically  at  the 
centre  of  the  horizontal  divided  circle  of  a  DeleuiPs  goniometer, 
the  telescope  of  which  was  replaced  by  the  polariscope  used  in 
the  preceding  observations.  The  latter  was  so  placed  that  iu 
axis  was  perpendicular  to  the  surface  of  the  bundle  when  the 
index  of  the  goniometer  was  at  zero.  With  the  instrument  thus 
adjusted  no  bands  are  seen  when  unpolarized  light  is  passed 
through  it ;  but  on  turning  the  glass  plates  bands  become  visible 
corresponding  to  polarization  in  a  vertical  plane.  The  amount 
of  the  light  polarized  by  refraction  through  four  glass  plates  at 
different  incidences  has  been  calculated  by  Professor  W.  G. 
Adams*  for  intervals  of  6^  from  10°  to  70°,  and  at  72°.  Taking 
the  values  given  in  his  Table  for  crown  glass  ()b(=sl*5),  those  for 
intermediate  angles  are  readily  determined  by  interpolation,  or 
graphically.    The  latter  method  was  employed,  a  curve  being 

*  Monthly  Notices  of  the  Royal  Astronomical  Society*  March  10, 1871, 
p.  162. 

Phil.  Mag.  S.  4.  Vol  48.  No.  815.  July  1874.  C 


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18  Prof.  A.  W.  Wright  on  the  Polarization 

drawn  representing  all  the  values  in  the  Table.  The  results 
given  in  the  Table  correspond  very  well  with  those  obtained  by 
Professor  Pickering*,  who  verified  his  values  experimentally, 
and  showed  that  the  deviation  from  theory  in  the  case  of  four 
plates  only  becomes  perceptible  above  65^.  As  Professor  Pick- 
ering  used  the  value /a =1 '55,  the  numbers  in  his  Table  are 
slightly  greater  than  those  used  in  constructing  the  curve  from 
Professor  Adams's  Table. 

The  determinations  were  made  by  observation  of  the  percent- 
age necessary  to  render  the  bands  visible  with  the  same  distinct- 
ness as  in  the  zodiacal  light.  A  set  of  experiments  were  made 
with  light  from  the  clear  sky  in  a  moonless  night,  the  instrument 
being  directed  to  one  of  the  brightest  points  of  the  galaxy, 
where  the  light,  though  less  bright  than  that  of  the  zodiacal 
light,  did  not  very  greatly  diflFer  from  it  in  intensity.  The  glass 
plates  being  turned  until  the  bands  had  the  same  degree  of  di- 
stinctness as  in  the  previous  observations,  the  mean  of  several 
observations  gave  as  the  polarizing  angle  41^,  corresponding  to 
a  percentage  of  20*5.  This  value,  on  account  of  the  inferior 
brightness  of  the  light  compared,  is  somewhat  too  large,  and 
may  be  taken  as  an  upper  limit. 

To  find  a  lower  limit  and,  at  the  same  time,  an  approximate 
value,  light  reflected  from  a  nearly  white  wall  with  a  dead  sur- 
face was  employed.  The  point  observed  with  the  instrument 
was  so  chosen  as  to  be  equally  distant  from  two  gas-flames  so 

f>laced  that  the  planes  through  them  and  the  axis  of  the  po- 
ariscope  were  at  right  angles,  thus  giving  light  entirely  free 
from  polarization.  The  flames  were  now  turned  down  equally, 
so  that  the  field  had,  as  nearly  as  could  be  estimated,  the  same 
brightness  as  it  had  with  the  zodiacal  light.  A  small  scratch 
upon  the  quartz  plate,  which  could  just  be  seen  by  the  light  of 
the  latter,  served  as  a  means  of  control  in  adjusting  the  inten- 
sity. The  experiments  being  conducted  as  before,  gave,  as  the 
mean  of  numerous  determinations,  the  angle  86^*6,  correspond- 
ing to  a  proportion  of  16  per  cent.^  which  is  probably  not  far 
from  the  true  value  of  the  amount  sought.  Another,  in  which 
the  light  was  made  perceptibly  brighter  than  that  of  the  zodiacal 
tract,  gave  for  the  angle  28^*5,  and  a  percentage  of  9*4,  which 
is  certainly  too  small.  We  may  safely  take  15  per  cent,  as  near 
the  true  value. 

The  fact  of  polarization  implies  that  the  light  is  reflected, 
either  wholly  or  in  part,  and  is  thus  derived  originally  from 
the  sun.  The  latter  supposition  is  fully  confirmed  by  various 
spectroscopic  observations,  of  M.  Liais  f.  Professor  C.  Piazzi- 

*  Silliman's  American  Journal,  S.  3.  vol.  vii.  p.  102. 
t  Comptes  Rendus,  1872,  vol.  Ixxiv.  p.  262. 


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of  the  Zodiacal  Light.  19 

Smyth 'i'^  and  others^  which  show  that  the  spectram  is  continuous, 
and  not  perceptibly  di£ferent  from  that  of  faint  sunlight.  The 
writer  has  also  made  numerous  observations  with  a  spectroscope 
specially  arranged  for  faint  light,  of  which  an  account  will  be 
published  hereafter,  and  which  lead  to  the  same  conclusion.  It 
may  be  mentioned  further  that  a  particular  object  in  these  ob- 
servations was  to  determine  whether  any  bright  lines  or  bands 
were  present  in  the  spectrum,  or  whether  there  is  any  connexion 
between  the  zodiacal  light  and  the  polar  aurora ;  and  the  results 
give,  as  an  answer  to  the  question,  a  decided  negative.  This  is 
important  here,  as  excluding  from  the  possible  causes  of  the 
light  the  luminosity  of  gaseous  matter,  either  spontaneous  or 
due  to  electrical  discharge.  The  supposition  that  the  light  is 
reflected  from  masses  of  gas,  or  from  globules  of  precipitated 
vapour,  is  not  to  be  entertained,  since,  as  Zollnerf  has  shown, 
such  globules  in  otherwise  empty  space  must  evaporate  com- 
pletely, and  a  gaseous  matter  would  expand  until  its  density 
became  far  too  small  to  exert  any  visible  effect  upon  the  rays  of 
light. 

We  must  conclude,  then,  that  the  light  is  reflected  from  mat- 
ter in  the  solid  state — that  is,  from  innumerable  small  bodies 
revolving  about  the  sun  in  orbits,  of  which  more  lie  in  the 
neighbourhood  of  the  ecliptic  than  near  any  other  plane  passing 
through  the  sun.  Although  such  a  cause  for  the  zodiacal  light 
has  often  been  assumed  as  probable,  no  satisfactory  proof  of  it 
has  hitherto  been  found ;  and  the  establishment  of  the  fact  of 
polarization  was  necessary  to  its  confirmation,  since  spectroscopic 
appearances  alone  leave  it  uncertain  whether  the  matter  is  not 
self-luminous. 

If  these  meteoroids,  as  there  is  no  good  reason  to  doubt,  are 
similar  in  their  character  to  those  which  have  fallen  upon  the 
earth,  they  must  be  either  metallic  bodies,  chiefly  of  iron,  or 
stony  masses  with  more  or  less  crystalline  structure  and  irre- 
gular surfaces.  If  we  accept  Zollner's  conclusion  that  the 
gases  of  the  atmosphere  must  extend  throughout  the  solar  sys- 
tem, though  in  an  extremely  tenuous  condition  in  space,  the 
oxidation  of  the  metallic  meteoroids  would  be  merely  a  question 
of  time.  They  would  thus  become  capable  of  rendering  the 
light  reflected  from  them  plane-polarized ;  and  the  same  effect 
would  in  any  case  be  produced  by  those  of  the  stony  character. 

In  order  to  ascertain  whether  the  proportion  of  polarized  light 
actually  observed  approached  in  any  degree  what  might  be  ex- 
pected from  stony  or  earthy  masses  of  a  semicrystalline  cha- 
racter with   a   granular  structure   and  surfaces  more  or  less 

*  Monthly  Notices  of  the  Royal  Astronomical  Society,  June  1872,  p.  277* 
t  l/«6er  die  Natur  der  Cometen,  p.  79  ^t  seq. 

C2 


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20  On  the  Polarization  of  the  Zodiacal  Light* 

rough,  a  large  number  of  substances  possessing  these  charac- 
teristics were  subjected  to  examination  with  a  polarimeter.  For 
this  purpose  the  apparatus  already  described  was  employed, 
there  being  added  to  it  a  support  for  the  object,  with  a  hori- 
2ontal  circle  for  determining  the  azimuths  in  placing  the  object 
and  the  light.  The  substances  examined  had  approximately 
plane  surfaces,  which  were  placed  vertically  and  so  that  the 
normal,  at  the  point  observed,  bisected  the  angle  between  the 
lines  from  it  to  the  eye  and  the  illuminating  flame.  The  light 
being  thus  polarized  in  a  horizontal  plane,  was  depolarized  (that 
is,  compensated)  by  turning  the  glass  plates  through  the  neces- 
sarv  angle,  the  percentage  corresponding  to  which  was  immedi- 
ately found  by  means  of  the  curve. 

If  we  suppose  a  line  drawn  from  the  place  of  observation  to  a 
point  in  the  zodiacal  light,  and  another  drawn  from  the  sun  to 
this  at  its  nearest  point,  the  two  lines  would  meet  at  right 
angles ;  and  a  surface  at  the  point  of  intersection  must  be  so 
placed  as  to  have  an  incidence  of  45^  in  order  to  send  the  re- 
flected light  to  the  eye  of  the  observer.  We  may  in  general 
assume  that  there  would  be  as  many  meteoroids  on  the  nearer 
side  of  the  line  from  the  sun  as  on  the  other.  Those  on  the 
more  remote  side,  while  presenting  a  larger  illuminated  surface, 
would  reflect  the  light  at  a  smaller  angle,  and  therefore  polarize 
a  smaller  amount  of  it.  Those  on  the  earthward  side  would 
send  less  light  to  the  earth,  but  polarize  a  larger  proportion  of 
it.  The  differences  would  so  nearly  complement  one  another 
that  we  may  take  their  united  effect  as  equivalent  to  that  of  a 
body  placed  at  the  point  of  intersection  mentioned  above.  For 
this  reason  the  objects  tested  were  so  placed  that  the  angles  of 
incidence  and  reflection  were  45°. . 

Some  of  the  substances,  and  the  percentages  obtained,  were 
as  follows : — ^Porphyry,  ground  smooth  but  not  polished,  35  per 
cent. ;  another  surface  thickly  covered  with  accumulated  dust, 
16*5 ;  dark  blue  shale,  25*7 ;  syenite,  coarsely  crystalline  and 
rough,  16'4;  gneiss,  rather  fine-grained,  8*8;  granite,  fine- 
grained, 11*8;  red  jasper,  rough  broken  surface,  23*5;  sand- 
stone 12*1 ;  brick,  rough  fragment,  8*1 ;  the  same,  smooth  sur- 
face, 11*3;  red  Wedgewood  ware,  unglazed,  14*2;  indurated 
clay,  light  brown,  11;  mortar,  whitewashed  surface,  12*1;  the 
same,  rough  side^  6 ;  white  chalk,  cut  plane,  2.  A  fragment  of 
the  great  meteorite  of  Pultusk,  which  the  writer  owes  to  the 
kindness  of  Professor  0.  C.  Marsh,  gave  from  a  broken  surface 
11*7,  from  the  blackened  surface,  36  percent,  of  polarized  light. 
It  is  of  the  stony  class,  and  of  a  light  bluish  grey  colour. 

The  results  show  that  from  surfaces  of  this  nature  the  light 
reflected  has  in  general  but   a  low  degree  of  polarization,  not 


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On  the  Constant  Currents  in  the  Air  and  in  the  Sea.       21 

greatly  different,  on  an  average,  from  that  found  in  the  zodiacal 
light.  Although  no  certain  conclusions  can  be  drawn  from  ex- 
periments like  these^  their  results  are  not  inconsistent  with  the 
supposition  in  reference  to  which  they  were  made,  but,  so  far  as 
they  go,  tend  to  confirm  it.  The  results  of  the  investigation 
may  be  summarized  as  follows : — 

1.  The  zodiacal  light  is  polarized  in  a  plane  passing  through 
the  sun. 

2.  The  amount  of  polarization  is,  with  a  high  degree  of  pro- 
bability, as  much  as  15  per  cent,  but  can  hardly  be  as  much  as 
20  per  cent. 

8.  The  spectrum  of  the  light  is  not  perceptibly  different  from 
that  of  sunlight,  except  in  intensity. 

4.  The  light  is  derived  from  the  sun,  and  is  reflected  from 
solid  matter. 

5.  This  solid  matter  consists  of  small  bodies  (meteoroids) 
revolving  about  the  sun  in  orbits  crowded  together  toward  the 
ecliptic. 

Yale  CoUege,  April  6, 1874. 


IV.  7%^  Constant  Currents  in  the  Air  and  in  the  Sea :  an  At- 
tempt  to  refer  them  to  a  common  Cause.  By  Baron  N.  Schil- 
ling, Captain  in  the  Imperial  Russian  Navy*. 

Introduction. 

THE  currents  of  the  sea  and  of  the  atmosphere  have  been 
observed  from  times  immemorial ;  much  has  been  written 
on  both  ;  but,  unfortunately,  science  has  hitherto  made  but  very 
unsatisfactory  progress  in  this  department.  The  laws  which 
govern  them  are  still  very  little  understood ;  and  their  origina- 
ting causes,  in  particular  those  of  the  great  ocean -currents  and, 
indeed,  of  the  trade-winds,  are  as  good  as  totally  unexplored, 
since,  on  closer  examination,  every  explanation  yet  given  must 
be  regarded  as  not  at  all  sufficient.  A  complete  knowledge  and 
u  comprehensive  theory  of  all  currents  will  long  remain  impos- 
sible, because  the  currents  are  subject  to  the  action  of  very 
various  influences,  and  these,  accompanied  by  very  manifold  cir- 
cumstances, exhibit  themselves  in  such  different  fashions  and 
are  so  complicated  that  it  has  not  hitherto  been  possible  to  sub- 
mit them  to  exact  mathematical  analysis.  Apart  from  the  theo- 
retical difficulties,  practice  often  opposes  insuperable  obstacles 
when  we  wish  to  trace  a  current  through  the  whole  extent  of  its 

*  Tranilated  from  a  separate  publication  commuiiicated  by  the  author, 
entitled  Die  bestandigen  Strdmungen,  &c.,  Berlin,  1874. 


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22  Baron  N.  Schilling  on  the  Constant  Currents 

course*  The  air-currents  escape  our  observations  in  the  upper 
strata  of  the  atmosphere^  and  those  of  the  sea  in  the  depths  of  the 
ocean*  Notwithstanding  all  the  improvements  of  nautical  instru- 
meuts,  we  still  possess  no  means  of  accurately  determining  the 
currents  at  sea.  Usually  the  ship's  reckoning  (f .  e.  the  distance 
run  in  a  certain  direction)  is  proved  from  time  to  time  by  astro- 
nomical determinations  of  latitude  and  longitude ;  and  the  dif- 
ference thus  brought  to  light  is  without  hesitation  attributed  to 
currents,  although  it  may  often  result  from  quite  different  causes. 
Although  the  unsatisfactoriness  of  this  method  has  long  been 
acknowledged^  it  is  still  universally  retained  for  want  of  a 
better. 

The  currents  of  the  sea  and  those  of  the  atmosphere  have 
hitherto  been  considered  apart — ^probably  because  water  and  air 
are^  in  many  respects,  so  very  different ;  but,  in  spite  of  this 
great  difference,  there  can  be  no  doubt  that  the  movements  of 
the  sea  and  of  the  atmosphere,  as  fluids,  are  subject  to  the  same 
general  laws.  For,  in  air  as  well  as  in  water,  gravity  is  the 
force  which  generates  currents,  because  it  tends  to  restore  equi- 
librium wherever  it  has  been  disturbed.  But  equilibrium  is 
disturbed  only  by  the  following  three  principal  causes,  which, 
again,  are  the  same  for  sea  and  air : — 

A.  Alteration  of  the  specific  gravity  of  the  water  or  air ; 

B.  The  rotation  of  the  earth  on  its  axis ; 

C.  The  attraction  of  the  sun  and  moon. 

We  see,  then,  that  the  currents  of  the  sea  and  the  air  depend 
on  the  same  principal  causes,  and  hence  cannot  well  be  separated 
in  the  consideration  of  their  theory ;  only  the  following  circum- 
stances must  be  kept  in  view. 

1.  The  air  is  a  highly  elastic,  readily  expanding,  gaseous 
body,  while  water  is  almost  entirely  destitute  of  elasticity. 

2.  The  atmosphere  is  heated  by  the  sun  principally  in  the 
lower  strata,  causing  them  to  expand,  become  lighter,  and,  as- 
cending, communicate  their  heat  to  the  higher.  The  sea,  on 
the  contrary,  is  heated  by  the  sun's  rays  on  its  surface  only  to 
a  very  slight  depth,  and,  in  consequence  of  evaporation,  gives  up 
the  greater  part  of  its  heat,  as  latent  heat,  to  the  air. 

3.  In  the  atmosphere  we  mostly  observe  only  the  currents  of 
the  lower  strata,  and  pay  little  attention  to  the  upper  currents, 
though  the  latter  are  often  very  different,  both  in  direction  and 
velocity,  from  the  lower.  In  the  water,  on  the  other  hand,  we 
direct  our  attention  mostly  to  the  upper  currents;  and  only 
quite  recently  have  temperature-determinations  at  greater  depths 
begun  to  throw  a  scanty  light  on  the  deeper  currents  of  the 
ocean. 

4.  The  seas  are  bounded  by  continents,  which  set  impassable 


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in  the  Air  and  in  the  Sea.  28 

lifluts  to  the  currents^  and  thereby  exert  great  influence  on  their 
direction,  extension,  and  velocity.  It  is  quite  otherwise  with 
the  atmosphere,  which  encompasses  the  globe,  and  is  undisturbed 
in  its  free  motion,  save,  perhaps,  in  some  degree  by  lofty  moun- 
tain-ranges. But,  on  the  other  hand,  currents  may  arise  in  the 
atmosphere  through  the  influence  of  the  interior  parts  of  the 
continents,  to  which  the  sea  has  nothing  to  correspond. 

Lastly,  mention  should  be  made  of  a  certainly  only  conventional 
difference  between  air-  and  ocean-currents.  This  is,  that  the 
winds  are  universally  named  after  the  point  from  which  they 
come,  while  ocean-currents  always  bear  the  name  of  the  point 
toward  which  thev  flow.  This  difference  of  nomenclature  ap* 
pears  at  first  sight  inconvenient;  but  use  has  so  naturaliied 
these  designations  in  all  languages  that,  as  Laughton^  quite  cor- 
reetly  remarks,  any  attempt  to  alter  this  custom  would  ouly  give 
rise  to  misunderstandings.  To  impress  this  upon  young  sailors, 
the  following  phrase  is  used  in  the  Russian  navy  : — *^  The  wind 
blows  to  the  card ;  currents  flow  from  the  card.'' 

The  differences  just  mentioned  between  the  air  and  water  ex- 
plain why  the  currents  in  the  atmosphere  often  appear  to  us 
quite  different  from  those  of  the  ocean,  since  the  two  classes  of 
currents  are  exposed  to  the  action  of  so  manv  and  various  colla- 
teral circumstances  that  the  community  of  their  fundamental 
laws  can  almost  be  no  longer  discovered.  And  yet  we  must  be 
clear  about  these  fundamental  laws  before  we  can  enter  upon  the 
consideration  of  the  collateral  actions. 

The  constancy  with  which  the  great  ocean-currents  and  the 
trade-winds  move,  and  the  analogy  which  prevails  between  them, 
justify  us  in  believing  that  they  are  less  exposed  to  the  opera- 
tion of  secondary  causes  and,  therefore,  are  especially  adapted 
for  the  study  of  the  general  laws  of  currents.  Hence  we  will 
examine  singly  the  above-named  three  causes,  which,  to  our 
knowledge,  are  alone  capable  of  disturbing  the  equilibrium  of 
the  sea  and  the  atmosphere.  We  will  ascertain  how  far  each  of 
them  is  to  be  regarded  as  a  generator  of  the  constant  sea-cur- 
rents and  the  trade-winds,  and  in  what  measure  it  answers  to 
the  existing  explanations  of  these  currents.  The  shifting  winds 
and  smaller  coast-currents  we  will  in  general  leave  unnoticed, 
because  (as  already  said)  our  information  is  still  much  too 
limited  for  us  to  be  able  to  form  even  the  remotest  idea  of  a 
theory  embracing  all  currents. 

However,  before  we  come  to  the  examination  of  the  forces 
which  call  forth  the  constant  currents,  we  will  briefly  describe 
the  great  oceanic  currents  and  the  trade- winds,  and  indicate  how 

*  Physical  Geography  (London,  1870),  p.  176. 

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24  Baron  N.  Schilliug  an  the  Constant  Currents 

the  origination  of  these  natural  phenomena  is  at  present  ac- 
counted for. 

Constant  Currents  and  Trade-winds,     Views  hitherto  held  on 
their  origin. 

The  analogy  which  subsists  between  the  constant  currents  of 
the  different  oceans,  as  well  as  between  the  trade-winds  and  the 
equatorial  currents,  is  most  striking. 

Both  in  the  Atlantic  and  in  the  Pacific  and  Indian  Oceans 
there  flows  from  east  to  west,  on  each  side  of  the  equator,  a  cur- 
rent extending  over  about  20  degrees  of  latitude*  and  many 
thousand  feet  deep.  This  is  named  the  equatorial  current^ 
while  for  more  particular  designations  the  names  of  the  ocean 
and  hemisphere  in  question  are  added.  Between  these  two 
equatorial  currents,  there  is  found  in  all  three  oceans,  nearly  on 
the  equator,  a  relatively  narrow  zone,  in  which  either  no  current 
or  one  flowing  in  the  opposite  direction  is  observed.  The  equa- 
torial streams  continue  their  westward  course  till  they  encounter 
coasts,  which  turn  aside  their  direction,  according  to  the  posi- 
tion of  the  coasts,  and  give  them  a  more  or  less  meridional  direc- 
tion, until,  in  both  hemispheres,  in  the  vicinity  of  40^  lat.  they 
turn  eastward  to  intersect  the  ocean  again  in  this  direction* 
This  latter  stream,  flowing  from  west  to  east,  pretty  well  takes 
in  a  zone  of  10  degrees  of  latitude,  and  in  all  the  oceans  and 
both  hemispheres  is  met  with  between  the  40th  and  50th 
parallels.  This  stream  has  different  denominations  in  different 
oceans ;  but  Miihry  gives  it  the  general  name  of  the  equatorial- 
compensation  stream ;  for,  arrived  at  the  eastern  boundary  of 
the  ocean  in  question,  the  stream  turns  back  again  into  the 
equatorial  region,  to  begin  afresh  its  westward  course.  In  this 
way,  in  each  hemisphere,  regular  circulations  are  formed,  which 
are  comprehended  under  the  denomination  of  rotation-currents. 
In  the  centre  of  these  circulations,  about  in  the  region  of  the 
80th  degree  of  latitude,  there  is  in  all  the  oceans  a  broad  strip 
in  which  no  current  is  observed,  and  which  is  known  by  the 
name  of  the  Sargasso-sea.  To  these  currents  parallel  to  the 
equator,  with  their  included  streamless  zones,  the  trade-winds 
with  their  zones  of  calms  exactly  correspond.  On  each  side  of 
the  equator  there  is  a  zone  from  16  to  20  degrees  broad  in  which 
a  constant  trade- wind  blows  in  the  principal  direction  of  east  to 
west.  In  the  vicinity  of  the  polar  boundary  of  this  zone  the  di- 
rection of  the  wind  is  indeed  mostly,  in  the  northern  hemisphere, 
from  the  north-east — and  in  the  southern,  from  the  south-east. 
In  the  middle  latitudes,  chiefly  between  the  40th  and  50th 

*  In  the  Indian  Ocean  the  northern  equatorial  current,  interrupted  by 
the  south  coast  of  Asia,  has  less  breadth. 


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in  the  Air  and  in  the  Sea.  25 

parallels^  therefore  entirely  as  with  the  compensation-currents, 
constant  west  winds  prevail,  under  the  name  of  anti-trades. 
Between  these  constant  air-currents  there  are,  just  as  with  the 
'  sea-currents,  both  in  the  vicinity  of  the  equator  and  not  far  from 
the  80th  degree  of  latitude  in  both  hemispheres,  zones  of  no 
wind,  which  are  known  by  the  name  of  the  equatorial  and  the 
tropical  calms.  The  trade-winds,  with  the  calm-zones  belonging 
to  them,  shift  a  little  with  the  seasons — ^in  the  summer  of  the 
northern  hemisphere  moving  somewhat  northward,  and  in  the 
winter  toward  the  south.  In  the  currents  of  the  ocean  this 
shifting  of  the  zones  is  less  marked;  hence  the  currents  of 
water  and  air  do  not  exactly  correspond ;  yet,  excepting  slight 
deviations,  the  trade-winds  with  their  calms  present  the  same 
picture  as  the  equatorial  currents  with  their  streamless  zones. 
In  spite,  however,  of  this  striking  similarity,  the  trade- winds 
have  till  now  been  ascribed  to  quite  different  causes  from  those 
of  the  gre-at  rotation-currents  of  the  ocean. 

We  shall  presently  return  to  this  subject;  we  will  now  only 
mention  further  that  the  rest  of  the  great  currents  in  the  dif- 
ferent oceans  likewise  correspond  so  completely  that  the  exist- 
ence of  very  determinate  laws  must  thence  be  inferred.  Thus 
the  Gulf-stream  and  the  Japanese  Kurosiwo  exhibit  precisely 
the  same  phenomena  :  both  are  currents  of  warm  water,  flow  in 
a  north-easterly  direction,  and  are  separated  from  the  coast  to 
the  west  of  their  course  by  a  cold  current  flowing  in  the  oppo- 
site direction.  The  cold  current  of  Peru  corresponds  to  that  of 
South  Guinea,  just  as  does  the  warm  Brazilian  current  to  that 
of  Mozambique.  Lastly,  a  feeble  current  from  south-west  to 
north-east  prevails  in  the  entire  south  polar  sea. 

The  trade- winds  have  from  the  17th  century  been  represented 
as  polar  winds  which  are  deflected  from  the  direction  of  the  meri- 
dian by  the  earth^s  rotation  :  this  theory  was,  as  far  as  we  know, 
first  set  up  (very  imperfectly,  it  is  true)  by  Varenius,  in  1660; 
it  was  subsequently  improved  by  Halley  in  1686,  and  Hadley 
in  1785,  and  is  for  the  most  part  named  after  the  latter,  as  it 
has  since  made  no  advance.  That  this  theory  has  been  so  gene- 
rally accepted  is  so  much  the  more  surprising,  as  many  pheno- 
mena of  the  trade-winds  are  scarcely  in  accordance  witn  it. 

According  to  this  theory,  the  masses  of  air  in  the  equatorial 
regions,  rendered  lighter  by  heating,  are  continually  ascending, 
through  which  the  cooler  and  heavier  air  of  higher  latitudes  is 
impelled  to  flow  toward  the  equator.  As  the  velocity  of  rota- 
tion is  greater  at  the  equator  than  at  any  other  latitude,  and 
gradually  diminishes  to  the  poles,  while  the  air-particles  (by  the 
law  of  inertia)  do  not  at  once  take  up  this  greater  velocity  as 
soon  as  they  arrive  at  parallel  circles  where  the  motion  is  more 


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26  Baron  N.  Schilling  im  the  Constant  Currents 

rapid,  the  polar  wind  is  turned  westward,  and  expresses  itself  in 
the  northern  hemisphere  by  a  north-east,  in  the  southern  by  a 
south-east  wind.  In  the  higher  strata  the  ascending  air  returns 
to  the  poles  to  serve  as  a  compensation  for  the  air  which  has 
flowed  thence  to  warmer  latitudes.  As  this  upper  anti-trade 
streams  polewards,  it  receives  from  the  rotation  of  the  earth  a 
deflection  eastward  in  both  hemispheres.  Compressed  by  cool- 
ing and  the  polar  convergence  of  the  meridians,  it  sinks  at  about 
the  latitude  of  80^  to  the  surface  of  the  earth  and  so  forms  the 
constant  west  wind  of  the  middle  latitudes.  The  ascent  of  the 
air  at  the  equator  and  its  descent  in  30°  lat.  will  produce  in  the 
first  case  the  equatorial  calms,  and  in  the  second  the  calms  of 
the  tropical  zones. 

This  is,  as  briefly  as  possible,  the  generally  recognised  theory 
of  the  trade-winds,  which,  however,  is  not  at  all  adapted  for  ex- 
plaining the  perfectly  analogous  rotation-currents  of  the  ocean. 

The  equatorial  current  is  still  regarded  by  manv  as  a  drift- 
stream  produced  by  the  trade-winds.  This  already  long-per- 
sistent opinion  received  such  a  confirmation  by  the  authority  of 
Franklin  and  Rennell,  that,  notwithstanding  its  forcible  refuta- 
tion by  Maury  and  MUhry,  it  is  still  maintained,  although  only 
in  England.  For  instance,  Herschel,  Carpenter,  and  Laugh- 
ton  have  recently  pronounced  in  favour  of  this  explanation. 
Far  more  prevalent,  however,  is  now  the  view  that  the  cause 
of  the  equatorial  current  is  to  be  sought  immediately  in  the 
axial  rotation  of  the  globe.  Columbus,  the  discoverer  of  this 
current  (in  1492),  accounted  for  it  by  the  universal  motion  of 
the  heavens  {con  los  ciehs)  from  east  to  west*.  This  notion  of 
the  ^'primum  mobile  ^'  was  followed  by  all,  till  Kepler  at  the 
commencement  of  the  17th  century  pointed  out,  and  Yarenius 
(1650)  proved  in  detail,  that  the  current  was  occasioned  not  by 
the  "primum  mobile/'  but  by  the  rotating  motion  of  the  earth, 
the  water  not  being  able  to  keep  up  with  the  earth^s  rapid  mo- 
tion. Miihry,  the  chief  authority  on  ocean-currents,  substanti- 
ally shares  this  view,  only  giving  to  it  a  different  and  not  quite 
intelligible  expression.  He  saysf*  as  Fourier  j:  before  him,  that 
the  staying  behind  of  the  water  is  effected  by  the  centrifugal 
force  of  the  earth.  By  this  expression  we  are  accustomed  to 
understand  the  force  that  throws  off  from  the  centre,  which 
always  acts  in  the  direction  of  the  radius  of  each  parallel  circle ; 
and  hence  we  cannot  see  how  this  force  could  cause  the  swift- 
ness of  rotation  of  the  water  to  be  less  than  the  rotation-velocity 
of  the  entire  globe. 

♦  Kohl,  Geschichte  des  OolfstromSt  p.  30. 

t  Ueber  die  Lehre  von  den  MeereS'Stromungeny  p.  5. 

J  Ann.  de  Chim,  et  de  Fky$.  1824,  p.  140. 


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m  the  Air  and  in  the  Sea.  27 

On  the  other  hand^  Miihry  accounts  for  the  compensation- 
corrent,  flowing  in  the  middle  latitudes  from  west  to  east,  by 
the  aspirating  or  attracting  force  of  the  equatorial  current — that 
is,  by  the  tendency  of  water  to  find  its  levels  which  impels  it  to 
fill  up  the  void  caused  by  the  primary  current.  He  therefore 
makes  the  aspirating  force  operate  in  a  vast  arc  across  the 
entire  ocean^  and  chiefly  between  the  40th  and  50th  parallels  of 
latitude — a  decided  circubu  vitiogus. 

The  meridional  currents*  are  mostly  accounted  for  by  the 
constant  difference  of  temperature  of  the  equatorial  and  polar 
re^ons ;  and  Miihry  attributes  to  the  cold  and  heavy  polar  flow 
the  primary,  and  to  the  warmer  and  lighter  compensating  anti- 
polar  flow  the  secondary  action.  At  the  same  time,  in  conse- 
quence of  the  velocity  of  the  earth^s  rotation  progressively  dimi- 
nishing in  the  direction  of  the  poles,  all  the  cold  or  polar  streams 
receive  a  deflection  of  their  direction  to  the  west,  and  the  warm 
autipolar  currents  a  deflection  eastward.  Franklin  and  Bennell 
explained  also  the  meridional  currents  by  the  action  of  the 
trade-winds ;  for  they  believed  that  by  the  driving  force  of  these 
winds  the  waters  are  accumulated  in  the  Gulf  of  Mexico  and 
are  discharged  in  the  Gulf-stream, — a  view  that  probably  now 
possesses  scarcely  any  adherents. 

Having  briefly  indicated  the  existing  explanations  of  the 
origin  of  the  great  ocean-currents  and  the  trade-winds,  we  will 
now  endeavour  to  ascertain  in  what  manner  each  of  the  three 
forces  before  mentioned  is  capable  of  acting  upon  the  currents, 
how  their  influence  must  express  itself,  and,  finally,  how  far  the 
explanations  hitherto  given  correspond  with  the  facts. 

A.  Alteration  of  the  Specific  Gravity  of  the  Water 
AND  Air. 

a.  Difference  of  Temperature. 
Every  material  substance  possesses  the  property  of  occupying 
a  greater  space  when  its  temperature  is  raised,  while  still  re- 
taining the  given  number  of  its  molecules  and  its  weight.  From 
this  it  follows  that,  after  a  rise  of  temperature  of  a  body^  fewer 
of  its  particles  can  find  room  in  a  given  space;  so  that  the 
specific  gravity  must  diminish  with  rise  of  temperature.  Sub- 
stances of  different  kinds  differ  widely  in  their  degrees  of  ex- 
pansion, and  hence  also  in  the  alteration  of  their  specific  gravity. 
According  to  determinations  by  Ermanf,  sea- water  expands 
0*00027  of  its  volume  with  every  degree  between  0**  and  12°  R. 
On  this  ground  it  has  been  calculated ;[  that  the  entire  mass  of 

^  These,  which  flow  in  the  direction  of  the  meridian,  Miihry  calls  lati- 
tudinal. T  Pogg.  Ann,  vol.  xz.  p.  114. 
I  Biflchof,  Lehrbuch  der  chem,  u,  phys.  Oeologie,  p.  7- 


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28  Baron  N.  Schilling  on  the  Constant  Currents 

equatorial  water  would  stand  14  feet  higher  than  the  water  of 
the  polar  seas^  if  it  could  not  flow  off.  It  has  been  thought 
that  this  tendency  of  the  equatorial  water- surface  to  rise  would 
serve  to  account  for  the  Gulf-stream^  which  accordingly  would 
flow  down  hill.  But  this  inconsiderable  elevation  of  the  surface 
of  the  equatorial  sea  would  not  give  a  fall  of  even  ^  inch  in  a 
German  mile,  which,  in  relation  to  the  velocity,  is  much  too 
little.  Even  the  assumed  elevation  of  the  surface,  however,  can 
never  actually  be  produced;  for  as  soon  as  any  particles  of 
water  become  a  little  lighter,  they  must,  in  obedience  to  the  law 
of  gravitation,  immediately  spread  uniformly  over  the  entire 
surface.  Thereby  is  necessarily  produced  a  flow  of  the  warmer 
and  therefore  lighter  superficial  water  to  the  colder  regions,  and 
of  the  heavier  cold  water  at  the  bottom  to  the  warmer  regions. 
Such  an  exchange  of  the  waters  of  the  warmer  and  colder  seas 
exists  in  reality.  A  proof  of  this  is  furnished  by  the  tempe- 
ratures of  the  ocean  diminishing  with  increasing  depth — the 
temperatures  of  the  greater  depths  being  very  low,  even  in  the 
equatorial  regions.  An  exception  to  this  rule  is  formed  by 
those  seas  which  are  divided  from  the  ocean  by  a  ridge  over 
which  the  water  is  considerably  less  deep.  In  such  seas  the 
temperature  sinks  merely  to  a  depth  corresponding  to  the  height 
of  the  water  above  the  ridge,  and  below  that  remains  nearly 
unaltered,  because  the  colder  water,  cut  off  by  the  ridge,  can 
have  no  influx.  We  have  an  example  in  the  Mediterranean, 
united  with  the  ocean  by  the  Straits  of  Gibraltar,  the  depth  of 
which  is  onlv  a  little  over  100  fathoms, — and  in  the  Skagerrack 
and  some  Norwegian  fjords,  for  which  the  bottom  of  the  pro- 
portionally much  shallower  North  Sea  forms  a  ridge.  It  is 
therefore  unquestionable  that  water  flows  at  the  surface  of  the 
sea  out  of  warmer  into  colder,  and  in  its  depths  out  of  colder 
into  warmer  regions ;  so  that  there  only  remains  to  get  an  idea 
of  the  velocity  of  these  currents. 

Water,  as  a  bad  conductor  of  heat,  is  warmed  only  very 
slowly,  and  expands  just  as  slowly.  Now,  as  this  expansion  is 
moreover  very  trifling,  the  streaming  produced  by  difference  of 
temperature  must  likewise  be  only  an  extremely  slow,  creeping 
motion. 

In  order  to  give  an  idea  of  the  origination  of  the  meridional 
currents  from  difference  of  temperature.  Dr.  Carpenter  showed, 
on  the  9th  January  1871,  at  the  Royal  Geographical  Society  in 
London,  the  following  experiment.  He  filled  a  glass  tank, 
several  feet  long,  with  water,  which  at  one  end  of  the  tank  he 
cooled  with  ice,  and  at  the  other  end,  bymeans  of  a  special 
arrangement,  he  heated  at  the  surface.  The  cooled  water  was 
coloured  red ;  the  heated,  blue.     At  the  close  of  the  lecture. 


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in  the  Air  and  in  the  Sea.  29 

which  may  have  lasted  an  hour^  the  blue  water  had  moved  along 
the  surface^  and  the  red  along  the  bottom ;  but^  notwithstanding 
the  pretty  considerable  difference  of  temperature  and  the  length 
of  time,  the  coloured  water  particles  had  travelled  only  a  few 
feet.  This  experiment  proves,  therefore,  only  what  we  have 
already  said — ^that  through  difference  of  temperature  an  ex- 
change of  the  water  particles  must  take  place,  but  that  this 
exchange  proceeds  verv  slowly,  even  with  considerable  difference 
of  temperature  and  with  little  distance  between  the  differently 
heated  waters. 

In  nature,  however,  the  difference  of  temperature  of  sea- 
water  is  proportionally  inconsiderable,  never  amounting  in  the 
whole  to  more  than  about  80^  C,  while  this  difference  is  dis- 
tributed over  the  vast  distance  of  the  polar  from  the  equatorial 
seas.  It  thus  appears,  then,  impossible  that  this  cause  can  have 
power  to  set  in  motion  such  a  current  as  the  Oulf-stream.  Even 
the  mass  of  the  heated  water,  which  is  so  readily  invoked,  cannot 
here  exert  any  accelerating  action,  because  only  an  incon- 
siderable superficial  layer  is  warmed  by  the  sun,  and  nothing 
hinders  the  direct,  gradual,  and  immediately  complete  inter- 
change of  the  water  particles.  Only  when  large  basins  of 
water  of  different  temperatures  are  united  by  a  channel  can  the 
mass  of  the  warmer  water  play  a  part,  and  the  difference  of 
temperature  generate  a  considerable  current  in  the  channel. 
Thus,  for  example,  we  may  regard  the  northern  part  of  the 
Atlantic  between  Norway  and  Greenland  as  a  broad  channel 
connecting  the  north-polar  basin  with  the  ocean. 

The  air,  however,  expands  15  times  as  much  by  heating  as 
water^  and  the  influence  of  temperature-difference  on  air- 
currents  is  undeniable ;  yet  even  here  that  influence  is  generally 
very  much  overrated.  For  air,  as  well  as  water,  is  a  bad  conductor 
of  heat,  and  therefore  only  slowly  changes  its  temperature  and 
therewith  its  specific  gravity.  Hence  we  are  decidedly  of 
opinion  that  the  expansion  of  air  by  heating  in  the  open  can  at 
most  occasion  only  a  gradual  inflow  of  air^  never  a  sudden  gust 
or  a  rapid  fall  of  the  barometer.  The  gradually  heated  air 
rises  only  gradually  and  slowly,  and  is  just  as  slowly  replaced 
by  cooler  air.  A  burning  light,  or  a  cbimney-fire  gives  us  the 
best  proof  of  the  correctness  of  this  assertion.  Although  the 
temperature  produced  in  the  fireplace  is  incomparably  higher 
than  ever  occurs  in  nature  through  the  heat  of  the  sun,  and  the 
draught  is  artificially  increased  by  the  height  and  narrowness 
of  the  flue,  yet  this  draught  is  so  inconsiderable  that  it  can 
seldom  carry  up  a  piece  of  paper  thrown  into  the  chimney,  and 
even  the  ashes  of  burnt  paper  are  hardly  lifted.  This  shows  us 
that  even  a  strong  heating  occasions  only  a  slow  ascent  of  the 


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80  Baron  N.  Schilling  on  the  Constant  Currents 

air ;  so  that  by  it^  at  all  events  in  ordinary  circumstances,  a 
breath  of  air,  but  no  wind,  can  be  produced.  In  a  forest-con- 
flagration, the  enormous  heat  appears  to  cause  a  considerable 
ascending  current  of  air;  but  even  then  the  inflow  of  air 
thereby  e£fected  is  perceptible  only  in  the  immediate  vicinity  of 
the  burning. 

Hence  we  believe  that  wind  can  mostly  arise  only  from  con- 
densation of  the  aqueous  vapours  in  the  atmosphere,  which 
possess  the  property  of  very  suddenly  changing  considerably 
their  degree  of  elasticity  and  the  pressure  resulting  from  it ; 
this  must,  of  course,  exert  a  great  influence  on  all  atmospheric 
phenomena.  Certainly  the  elasticity  of  the  aqueous  vapour 
stands  in  the  closest  relation  with  the  temperature,  which  so 
far,  therefore,  operates  indirectly  in  the  origination  of  wind. 
Whether  change  of  temperature  is  the  only  cause  of  the  con- 
densation of  vapour,  we  know  not :  as,  when  the  aqueous  vapours 
are  condensed,  electricity  is  always  set  free,  perhaps  conversely 
the  condensation  may  be  caused  by  electricity. 

At  any  rate  it  is  changes  in  the  tension  of  the  aqueous  vapour 
that  produce  strong  winds ;  and  only  in  very  peculiar  cases  can 
the,  by  itself,  slow  expansion  of  the  air  develop  stronger  winds. 
Thus,  for  instance,  when  the  greater  portion  of  a  continent  is 
powerfully  heated  by  the  sun,  the  mass  of  air  rising,  though 
only  slowly,  from  the  whole  of  the  vast  surface,  would  require 
for  its  replacement  (that  is,  for  the  restoration  of  equilibrium) 
such  a  mass  of  air  that  the  inflow  must  be  much  accelerated, 
because  it  forms  a  stratum  of  little  height  in  comparison  with 
the  magnitude  of  the  heated  surface.  An  example  of  winds 
thus  produced  is  afforded  by  the  monsoons.  Over  the  ocean  the 
atmosphere  can  never  be  so  much  heated  as  over  the  land ;  and, 
besides,  evaporation  of  the  water  of  the  sea  and  the  elasticity  of 
the  aqueous  vapour  are  augmented  as  the  temperature  of  the  air 
rises.  If,  therefore,  the  expansion  of  the  air  diminishes  the 
atmospheric  pressure,  on  the  other  hand  the  augmented  elasticity 
and  quantity  of  aqueous  vapour  will  again  increase  it ;  and  it  is 
difScult  to  decide  which  of  these  two  may  exert  the  greater  in- 
fluence. Admitting  that  the  diminution  of  the  atmospheric 
pressure  by  expansion  of  the  air  is  greater  than  the  rise  of  the 
pressure  by  aqueous  vapour^  it  yet  appears  to  us  self-evident 
that  the  wind  resulting  from  the  heating  of  a  continent  must  be 
much  stronger  than  that  produced  by  the  heating  of  the  air 
over  the  ocean,  supposing  both  to  take  place  over  very  consider- 
able spaces. 

If,  then,  the  recognized  theory  of  the  trade-winds  were  cor- 
rect and  they  were  produced  by  the  ascent  of  the  heated  air,  the 
trade- winds  would  blow  in  summer  towards  the  Sahara,  since 


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in  the  Air  and  in  the  Sea.  81 

there  the  thermometer  not  seldom  shows  50^  C.  in  the  shade^ 
while  in  the  equatorial  regions  of  the  ocean  the  temperature  of 
the  air  never  rises  above  30**  C.  The  trade-wind,  however,  at 
the  north-west  coast  of  Africa  blows  constantly  from  the  desert, 
carrying  the  fine  sand  far  out  to  sea. 

Farther,  in  summer  the  temperature  of  the  20th  and  30th 
degrees  of  latitude  is  not  lower,  indeed  it  is  higher  than  that  of 
the  equator,  and  yet  the  shifting  of  the  trade-zones  is  inconsi- 
derable, and  the  wind  keeps  its  usual  direction. 

Likewise,  according  to  Hadley's  theory  an  ascending  or  a  de- 
scending current  should  prevail  in  the  calm-zones.  Now  this 
current  must  be  very  considerable,  if  it  brings  forth  the  fresh- 
blowing  trades  and  anti-trades ;  and  the  ascent  of  the  air  in  the 
equatorial  calms,  and  its  descent  in  the  tropical  calms,  would 
make  themselves  perceptible,  even  if  the  motion  were  very  slow. 
This,  however,  is  not  the  case :  a  particle  of  dust  loosened  from 
the  sails  falls,  both  in  the  equatorial  and  the  tropical  calm-zone, 
quietly  to  the  deck,  without  exhibiting  the  slightest  tendency  to 
be  impelled  upward  or  downward.  From  this  we  conclude  that 
the  upward  and  downward  currents  of  air  in  the  zones  of  calms, 
if  they  really  exist,  must  be  so  slight  that  the  generation  of  the 
trade-winds  and  anti-trades  cannot  possibly  be  ascribed  to 
them. 

Let  it  further  be  remembered  that  in  the  middle  latitudes  of 
the  northern  hemisphere  the  anti-trade  often  blows  from  the 
north-west  instead  of  south-west,  and  in  the  southern  hemisphere 
from  south-west  instead  of  north-west — which  could  not  be,  if, 
as  required  by  Hadley^s  theory,  it  formed  a  current  directed 
toward  the  poles. 

Lastly,  in  Central  Europe  these  constant  west  winds  blow  in 
summer  very  moderately,  while  in  winter  their  force  is  much  in- 
creased— which  again  does  not  correspond  with  the  theory ;  for 
in  summer  the  eastern  steppes  are  strongly  heated  and  should 
attract  the  west  wind,  while  the  cold  which  prevails  in  Eastern 
Europe  in  winter  would,  on  the  contrary,  contribute  to  the 
weakening  of  the  west  wind. 

All  this  and  many  other  reasons'^  show  that  the  existing 
theory  of  the  trade-winds  is  not  sufficient  to  account  for  the 
phenomenon,  and  that  another  must  be  sought. 

We  do  not  on  this  account  dispute  that  heated  air  must 
ascend ;  we  only  believe  that,  since  the  heating  and  expansion 
proceed  very  gradually,  the  ascent  must  also  be  very  slow  and 
hence  cannot  constitute  the  principal  cause  of  the  trade-winds. 
Their  main  motive  cause  appears  therefore  to  lie  in  other  forces, 
of  which  we  will  speak  subsequently. 

*  Laughton,  'Phyrical  Geography,'  pp.  120-127. 


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82  Baron  N.  Schilling  on  the  Constant  Currents 

If,  then^  difference  of  temperature  can  only  call  forth  incon- 
siderable winds  by  the  expansion  of  the  air,  it  is  clear  that  in 
water,  so  much  less  expansible,  heated  to  only  a  proportionally 
slight  depth,  no  great  current  can  be  generated  by  this  cause. 
If  this  force  were  sufficient  to  occasion  a  considerable  current,  it 
would  extend  over  the  entire  surface  of  the  ocean,  and  not  merely 
show  itself  in  a  narrow  strip  at  its  margin. 

We  nevertheless  allow  that  the  heating  of  the  water  may,  in 
certain  cases,  have  an  important  influence  on  the  maintenance 
and  extension  of  an  already  existing  current.  If,  e.  g.,  a  cur- 
rent arising  from  other  causes  strikes  upon  a  coast,  it  usually 
takes  the  direction  of  this  coast,  along  which  it  continues  until 
it  gets  beyond  the  sphere  of  the  action  to  which  it  owes  its  de- 
velopment. But  if  it  accumulates  at  the  coast  the  heated  sur- 
face-water of  the  sea,  the  mass  of  warmer  and  lighter  water, 
continually  replaced,  will  perpetually  exhibit  the  endeavour  to 
spread  over  the  heavier  water  of  colder  regions.  Difference  of 
temperature  will  therefore  in  this  case  have  an  essential  influence 
on  the  continuance  and  the  direction  of  the  currents  toward 
higher  latitudes,  but  cannot  independently  generate  the  currents. 
This,  then,  explains  to  us  also  how  it  is  that  warm  and  cold  cur- 
rents are  found  preeminently  at  sea-coasts.  The  first  impulse, 
however,  to  the  flowing  which  collects  the  heated  water  does  not 
arise  from  difference  of  temperature,  but  always  from  other 
causes.  The  ascertaining  of  these  initiating  causes  is  of  very 
great  importance  for  the  foundation  of  a  theory ;  for  without 
accurate  knowledge  of  the  fundamental  laws,  we  can  get  no 
account  of  the  action  of  the  accessory  causes. 

Let  us  now  consider  the  possible  influence  of  evaporation.  As 
already  said,  the  evaporation  of  water  is  in  close  connexion  with 
heat ;  for  with  a  rise  of  temperature  the  capability  of  the  air  to 
take  up  aqueous  vapour  is  also  increased.  Hence  much  more 
water  is  evaporated  in  the  equatorial  regions  than  in  higher 
latitudes;  and  the  vapours  are  driven  by  air-currents  into  other, 
cooler  regions,  where,  on  the  cooling  of  the  air,  they  are  given 
back  to  the  sea  as  an  atmospheric  precipitate.  Evidently  from 
this  cause  must  arise  a  sea-current  toward  the  equator,  though 
only  a  very  inconsiderable  one.  Miihry  calculates  that  in  the 
tropics  about  15  feet  of  water  evaporate  yearly,  therefore 
about  half  an  inch  daily.  Perhaps  half  of  this  evaporation  is 
returned  to  the  tropical  seas  as  rain  and  river-water,  and  only 
the  other  half  (J  inch  daily)  returns  by  sea-currents  from  higher 
latitudes.  But  a  current  which  in  the  course  of  24  hours  re- 
places only  a  layer  of  water  a  quarter  of  an  inch  in  thickness, 
must  be  imperceptible.  This  slight  current  flows  at  the  surface, 
and  is  directed  to  the  equator ;  it  thus  counteracts  the  current 


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m  tlie  Air  and  in  the  Sea,  ' .  83 

arising  from  difference  of  temperature,  which,  as  above  remarked, 
must  flow  at  the  surface  from  warmer  into  colder  zones. 

Evaporation,  then,  also  cannot  occasion  any  perceptible  cur- 
rent in  the  open  sea ;  but  in  channels  connecting  an  inland  sea 
with  the  ocean  a  diflerence  of  level  between  the  two  seas,  arising 
from  greater  evaporation  of  the  inland  sea,  may  occasion  a  strong 
current.  We  have  instances  of  this  in  the  Straits  of  Gibraltar 
and  Babelmandeb. 

Let  us  now  turn  to  the  consideration  of  the  influence  which 
heat  may  have  indirectly  on  the  origination  of  sea-currents 
when,  through  its  action  upon  the  aqueous  vapour  in  the  atmo- 
sphere^ it  generates  wind.  The  action  of  wind  upon  the  surface 
of  water  is  familiar  not  only  to  the  inhabitants  of  coasts,  but  to 
almost  every  one.  Indeed  we  see  in  every  pond  how  the  water 
is  driven  by  a  strong  wind ;  and  if  the  basin  is  flat  and  not  very 
deep,  not  seldom  does  the  water  recede  from  the  windward 
side,  and  accumulate  on  the  lee  side.  Such  heapingsup  of  the 
water  in  shallow  bays,  and  at  the  mouths  of  great  rivers,  by 
strong  winds  occasion  inundations.  At  a  straight  coast-line, 
too,  the  water  may  rise  considerably  by  the  force  of  the  wind, 
if  the  depth  inci*eaBe8  very  gradually  and  thereby  the  outflow 
beneath  is  checked. 

Indeed,  on  the  open  sea  the  wind  often  drives  the  water 
before  it,  and  thereby  forms  what  ai«  called  drift  or  superficial 
currents ;  but  these,  as  irregular  phenomena,  do  not  here  come 
into  consideration;  we  can  only  occupy  ourselves  with  those 
currents  which  are  called  forth  by  constant  winds,  t.  e,  the 
trade-winds.  Even  the  constant  action  of  the  trade-winds, 
however,  is  hardly  able  to  occasion  any  very  deep-going  current, 
as  has  already  been  sufficiently  shown  by  Maury  and  Muhry. 

According  to  FitzRoy^s  data,  the  highest  waves  rise  to  the 
height  of  60  feet*,  measured  from  the  trough  to  the  crest  of  the 
wave,  therefore  30  feet  above  the  smooth  surface  of  the  sea.  If 
we  might  assume  that  the  entire  wave  could  be  driven  forward 
by  the  wind  (which  is  decidedly  assuming  too  much),  thus 
would  be  produced  a  current  of  30  feet  depth.  Through  the 
friction  of  the  water-particles,  the  efiect  of  the  wind  upon  the 
current  may  become  sensible  somewhat  deeper  still ;  but  the 

*  This  number  appears  to  us  very  high ;  for  we  have  often,  in  a  severe 
storm,  ascending  the  shrouds,  tried  to  bring  our  eye  into  such  a  position 
that,  at  the  moment  when  the  ship  was  exactly  in  the  trough,  we  could 
see  several  wave-crests  in  a  hori2ontal  Hne.  The  height  of  the  eye  above 
the  ship's  water-line  then  determines  the  greatest  height  of  the  wave.  In 
this  way  J  have  only  once  at  Cape  Horn  (where  the  waves  rise  uncommonly 
high)  measured  a  height  of  46  feet,  and  at  the  coast  of  Japan,  in  a  typhoon, 
one  of  38-40  feet ;  at  other  times  the  height  was  mostly  less  than  this. 

P/uL  Mag,  S.  4.  Vol.  48.  No.  315.  July  1874.  D 


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34  Baron  N.  Schilling;  on  the  Constant  Currents 


b 


flowing  must  rapidly  diminish  downward^  and  soon  entirely 
cease.  A.  Findlay*  thinks  that  the  wind  can  never  call  forth 
a  current  of  greater  depth  than  5  fathoms.  James  Croll's  re- 
mark t>  that  the  duration  of  the  wind,  as  well  as  its  force,  must 
have  great  influence  on  the  depth  to  which  it  acts,  may  to  a 
certain  extent  be  quite  correct ;  but,  nevertheless,  action  of  the 
wind  upon  currents  at  a  depth  of  thousands  of  feet  (as,  for  in- 
stance, in  the  equatorial  current)  is  not  possible;  hence  we 
must  see  that  Franklin  and  Rennell's  view,  that  the  equatorial 
current  results  from  the  action  of  the  trade-winds,  cannot  be 
true. 

Nature  herself  gives  us  decisive  proofs  against  that  view. 
With  the  shifting  of  the  zone  of  calms  it  happens  that  the 
equatorial  current  flows  just  as  well  in  that  zone  as  in  the  trade- 
wind.  In  the  Indian  Ocean  the  change  of  the  monsoons  has 
scarcely  any  influence  on  the  equatorial  stream.  The  Gulf- 
stream  often  flows  in  opposition  to  very  violent  storms,  which 
would  be  impossible  if  its  motive  force  lay  in  the  trade-wind. 

Even  the  opinion  that  the  trade-wind  raises  the  level  of  the 
Gulf  of  Mexico,  and  so  produces  the  Gulf-stream,  is  untenable. 
In  the  flrst  place,  it  is  proved  by  the  levelling  of  the  isthmus  of 
Panama  and  the  peninsula  of  Florida  that  this  is  not  the  case, 
as  the  level  of  the  Mexican  Gulf  pretty  closely  accords  with 
both  that  of  the  great  ocean  and  that  of  the  Atlantic.  Secondly, 
in  the  open  sea  an  enduring  higher  level  can  never  be  product 
by  the  action  of  the  wind ;  for  as  soon  as  any  particles  of  water, 
driven  by  the  wind,  change  their  place,  they  compel  by  their 
pressure  just  as  many  others  immediately  to  take  the  place  lef^ 
free  by  them.  Only  where  the  formation  of  the  coast  hinders, 
or  at  least  impedes,  this  back-flowing  motion,  can  an  alteration 
of  level  take  place. 

Certainly  the  mechanical  pressure  of  the  wind  upon  the  sur- 
face of  the  water  can,  in  the  open  sea,  somewhat  alter  the  level ; 
but  as  the  wind  mostly  acts  horizontally,  or  at  a  very  acute 
angle,  upon  the  surface,  the  mechanical  pressure  is  so  little 
that  the  oscillations  of  the  sea-level  brought  about  by  it  must 
likewise  be  inconsiderable. 

Just  so  must  the  variations  of  the  atmospheric  pressure  exert 
an  influence  on  the  height  of  the  water  of  the  seas,  and  con- 
sequently also  on  their  currents.  When,  for  example,  the 
barometer  falls  an  inch,  the  surface  of  the  sea  at  the  place  must 
rise  13'6  inches,  and  vice  versd,  and  thus  a  current  be  formed 
from  where  the  pressure  is  high  to  the  region  where  lower  pres- 

♦  A  Dictionary  for  Navigation  of  the  Pacific  Ocean  (London,  1851), 
vol.  ii.  p.  1222.     Also  Miibry,  Geograph.  Mittheilungen,  1872,  p.  136. 
t  Phil.  Mag.  October  1871,  p.  2G8. 


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in  the  Air  and  in  the  Sea.  B5 

sure  prevails.  It  is  self-evident  that  a  current  thus  produced 
in  the  ocean  can  only  be  very  inconsiderable  and  inconstant, 
since  it  changes  with  every  change  of  the  atmospheric  pressure. 
This  foi-ce,  again,  can  only  make  itself  perceptible  in  channels. 

Suppose  that  on  an  inland  sea  connected  with  the  ocean 
only  by  a  strait  the  barometer  suddenly  fell  1  inch,  the  level  of 
this  sea  would  stand  13*6  inches  lower  than  equilibrium  with 
the  ocean  at  the  moment  would  require.  The  mass  of  water 
wanting  must  therefore  pass  from  the  ocean  through  the  strait. 

We  must  ascribe  it  to  this  circumstance  that,  in  the  Sound,  a 
change  in  the  direction  of  the  current  mostly  occurs  24  hours 
before  a  change  in  the  direction  of  the  wind.  Just  so  the  water 
usually  rises  in  the  Gulf  of  Finland  before  the  south-west  wind 
comm^ices;  and  this  rise  is  noticed  also  in  winter,  when  the 
entire  surface  of  the  sea  is  covered  with  ice,  and  thereby  the 
direct  action  of  the  wind  is  withdrawn. 

b.  Saltness  of  Sea-water. 

Alterations  in  the  saltness  of  seas  greatly  aflfect  the  specific 
gravity  of  the  water.  The  observations,  however,  which  have 
been  made  in  different  parts  of  the  world  have  proved  that  the 
difference  in  saltness  of  the  various  oceans  is  extremely  slight 'i^. 
This  compels  as  to  the  conclusion  that  currents  immediately 
tend  to  equalize  the  slightest  difference  in  the  saltness  of  the 
water. 

The  causes  of  change  in  the  saltness  may  be  accidental  and 
temporary,  or  constantly  repeating  themselves  in  certain  regions. 
In  the  first  case  they  produce  variable  currents,  which  do  not 
belong  to  the  subject  we  are  considering;  but  in  the  second 
they  must  confer  upon  the  water  a  constant  tendency  to  inter- 
change, and  call  forth  constant  currents. 

In  the  equatorial  regions^  for  example,  the  half  inch  of  water 
evaporated  daily  leaves  constantly  its  salt  behind,  which,  with 
the  vast  depth  of  the  ocean,  can  hardly  add  perceptibly  to  the 
specific  gravity  of  the  rest  of  the  water. 

Nevertheless  this  water,  very  gradually  becoming  slightly 
Salter  and  heavier,  and  sinking,  must  occasion  in  the  depths  a 
current,  although  a  very  feeble  one,  the  direction  of  which  must 
be  into  the  regions  where  there  is  little  evaporation  and  consider- 
able atmospheric  precipitation,  therefore  into  higher  latitudes. 
Consequently,  as  we  have  already  seen,  the  current  called  forth 
by  the  evaporation  of  the  water  counteracts  that  which  is  pro- 
duced by  the  expansion  of  the  water  from  difference  of  tem- 
perature. 

*  **  On  the  Composition  of  Sea-water  in  different  parts  of  the  Ocean," 
Pbil.  Trans.  Roy.  Sck?.  London,  1865.  ]).  203. 

D2 


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86  Baron  N.  Schilling  on  the  Constant  Currents 

In  the  polar  sea  much  water  is,  in  winter,  turned  into  ice, 
and  its  salt  separated.  This  salt  adds,  though  only  inconsider- 
ably, to  the  specific  gravity  of  the  cold,  and  hence  already  heavy, 
polar  water,  and^ebntributes  a  little  to  the  undercurrent  in  the 
dii*ection  of  the  equator ;  so  that  it  acts,  contrary  to  the  pre- 
ceding case,  just  the  same  as  the  difference  of  temperature. 
Perhaps  it  is  partly  owing  to  this,  that  the  flow  of  the  Gulf- 
stream  is  somewhat  stronger  in  winter  than  in  summer. 

In  an  extremely  interesting  article  on  the  currents  at  the 
southern  extremity  of  America,  Miihry*,  on  the  ground  of  the 
winter  temperature  of  Patagonia,  conjectures  that  the  Brazilian 
current  also  is  stronger  in  the  winter  of  the  southern  hemi- 
sphere than  in  summer. 

In  summer,  when  the  polar  ice  melts,  a  superficial  polar 
current  results;  for  the  water  from  the  melting  of  the  ice, 
having  but  little  saltness,  remains  at  the  surface  in  spite  of  its 
coldness.  Scoresby  remarked  that  near  Spitzbergen  the  water 
of  the  surface  was  warmer  than  at  some  feet  depth ;  and  this 
observation  has  been  recently  confirmed  by  the  Swedish  Expe- 
dition and  by  the  Norwegian  Captain  Ulvef* 

Unfortunately,  we  do  not  yet  possess  any  accurate  determina- 
tions of  the  greatest  density  of  sea-water  at  different  tempera- 
tures and  under  various  pressures.  At  all  events,  however, 
Miihry^s  view,  that  sea-water,  as  well  as  fresh  water,  attains  its 
greatest  density  at  -h4^C.,  appears  destitute  of  proof;  for  it 
has  recently  been  found  that  the  temperature  at  very  great 
depths  is  often  below  0^  C.  It  is  probable  that  the  great  pres- 
sure to  which  the  water  is  there  exposed  has  an  influence  in 
preventing  it  from  freezing,  even  below  0^  C.  If  earlier  obser- 
vations seem  to  contradict  this,  the  reason  may  well  be  that  the 
thermometers  were  not  sufficiently  protected  against  the  pres- 
sure of  the  depths,  and  hence  always  gave  the  temperature  of 
the  bottom  too  high.  On  this  defect  rests  also  Uoss's  well- 
known  theory  of  a  constant  temperature  of  -h39^  F.  at  the 
bottom  of  the  sea. 

At  the  mouths  of  rivers,  the  fresh  water  must  spread  upon 
the  surface,  and  therefore  give  rise  to  a  current  running  out- 
wards from  the  mouth,  until  it  is  mixed  sufficiently  with  the 
salt  water.  To  this  end,  however,  the  heavy  salt  water  will 
flow  in  the  opposite  direction,  toward  the  mouth — which,  even 
with  a  slight  current,  must  greatly  favour  the  formation  of 
sandbanks  there. 

In  the  case  of  inland  seas  where  the  inflow  is  greater  than  the 
evaporation,  as  ^.^.  in  the  Black  Sea  and  the  Baltic,  just  as 

*  Petermann's  Geographische  Miltheilungen,  1872^  vol.  xviii.  p.  12G. 


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in  the  Air  and  in  the  Sea.  87 

"With  rirer-mouths,  the  upper  current  in  the  channel  of  discharge 
will  flow  outwards,  while  an  undercurrent  of  constantly  salt 
water  must  flow  inwards.  But  in  seas  where  the  evaporation 
exceeds  the  influx  (for  example,  in  the  Mediterranean  and  the 
Red  Sea),  the  upper  current  must  flow  in  through  the  channel, 
and  the  undercurrent  carry  out  the  superfluous  salt.  An 
extremely  interesting  example  of  this  sort  is  presented  by  the 
Gulf  of  Karabughaz,  which  is  connected  with  the  Caspian  b^  a 
very  flat  channel  of  only  a  few  feet  depth.  As  the  evaporation 
from  the  very  spacious  surface  of  the  gulf,  into  which  no  streams 
flow,  is  very  great,  especially  in  summer,  water  is  perpetually 
flowing  in  from  the  Caspian  with  a  velocity  that  sometimes  rises 
to  6  knots  an  hour.  Of  course  this  current  brings  much  salt 
into  the  gulf,  from  which  it  cannot  get  out  again,  because  the 
channel  is  too  shallow  to  permit  an  outflow  beneath.  The  salt 
thus  accumulating  is  deposited  in  crystals  on  the  bottom;  and 
thus  the  Gulf  of  Karabughaz  plays  the  part  of  a  saltpan  conti- 
nually withdrawing  salt  from  the  Caspian  Sea.  If  in  the  course 
of  time  the  sand  washed  in  by  the  waves  should  completely 
block  up  the  shallow  strait  which  joins  the  gulf  to  the  sea  (which 
would  long  since  have  happened  if  the  current  were  not  so 
strong),  Karabughaz  as  a  lake  would  soon  evaporate  completely 
and  leave  behind  a  basin  of  solid  salt,  such  as  we  see  in  the 
Elton-See  and  in  lletzkaja  Saschtschita  as  formations  of  pri- 
meval times. 

If  in  any  part  of  the  ocean  animal  life  be  developed  in  greater 
abundance  than  in  others,  the  excessive  abstraction  of  salt  or 
lime  from  the  water  by  the  animals  will  also  give  rise  to  slight 
movements  of  the  water.  Although  such  movements  could 
scarcely  be  called  a  current,  it  cannot  be  doubted  that  such  must 
take  place  in  the  deepest  seas  even  at  the  bottom,  because  other- 
wise no  life  would  be  possible  there ;  for  among  the  animals 
living  in  the  depths  there  are  creatures  that  cannot  change  their 
place ;  nourishment  must  consequently  be  brought  to  them  by 
currents. 

The  theory  of  perfect  stillness  in  the  bottom  waters  of  the 
sea  *  is  therefore,  like  the  theories  of  Boss  and  Forbes,  to  be 
regarded  as  incorrect. 

We  have  thus  examined  all  the  causes  which  afiect  the  specific 
gravity  of  sea-water  and  the  air,  and  come  to  the  conclusion  thit 
differences  of  temperature  and  in  the  saltness  of  the  water  of  the 
sea  assist  only  in  a  slight  degree  in  maintaining  the  great  ocean- 
currents  and  the  trade-winds,  but  cannot  possibly  produce  them ; 

*  Miifiry  says,  "  At  the  bottom  of  the  ocean  we  must  assume  that  there 
is  almost  complete  stillness."— L^Are  uber  die  Metres- Stromungen,  p.  6. 


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38  Mr.  R,  Mallet  on  the  Tidal  Retardation 

to  explain  the  origiDation  of  these  currents  we  must  search  for 
other  forces. 

In  certain  cases,  if  an  already  existing  current  accumulates 
the  heated  water  in  greater  quautity,  the  diflFerence  of  tempera- 
ture may  indeed  accelerate  this  current ;  and  in  the  air,  if  it 
operates  over  very  considerable  spaces,  it  can  generate  wind ; 
but  in  general  it  is  the  quickly  condensing  aqueous  vapour 
which,  by  the  diminution  of  its  tension,  plays  the  chief  part  in 
the  production  of  wind. 

[To  be  continued.] 


V.  Tidal  Retardation  of  the  Earth's  Rotation. 
By  Robert  Mallet,  F,R,S.* 

THE  general  idea  of  the  retardation  of  the  earth's  rotation  by 
the  great  tide-wave  acting  as  a  friction-brake  as  it  pro- 
gresses under  the  coercion  of  the  moon,  commonly  ascribed 
to  Mayer,  was,  I  have  good  reason  to  believe,  anticipated  by 
Emanuel  Kant,  though  I  have  not  been  able  myself  to  verify  the 
passage  in  his  writings.  Of  the  real  existence  of  such  a  re- 
tarding force,  however  small  may  be  its  effect,  there  can  be  little 
doubt  since  the  masterly  researches  of  Adams  upon  the  moon's 
acceleration.  The  subject,  probably  from  its  inherent  complexity, 
has  attracted  but  little  attention,  except  from  astronomical 
mathematicians ;  and  some  points  respecting  it  which  have  been 
referred  to  in  more  popular  work8,  appear  involved  in  some  ob- 
scurity. Professor  Tyndall,  who,  in  his  'Heat  a  Mode  of  Motion,' 
gives  a  very  lucid  popular  account  of  the  phenomena  (almost, 
as  he  states,  in  the  words  of  Mayer),  has  in  paragraph  697> 
p.  483  (4th  edit.),  the  following  passage : — "  Supposing,  then, 
that  we  turn  a  mill  by  the  action  of  the  tide,  and  produce  heat 
by  the  friction  of  the  millstones ;  that  heat  has  an  origin  totally 
different  from  the  heat  produced  by  another  pair  of  millstones 
which  are  turned  by  a  mountain-stream.  The  former  is  pro- 
duced at  the  expense  of  the  earth's  rotation,  the  latter  at  the 
expense  of  the  sun's  heat  which  lifted  the  mill-stream  to  its 
source."  This  distinction,  it  seems  to  me,  cannot  be  main- 
tained. The  power  of  a  tide-mill  is  not  derived  from  the 
rotation  of  the  earth,  nor  from  the  retardation  of  that  rotation 
by  the  great  tide-wave.  The  sea,  no  matter  from  what  cause, 
rises  above  its  normal  level,  to  which  it  after  a  time  sinks  again. 
If  during  the  interval  we  can  impound  a  portion  of  the  mass  of 
water  so  elevated  and  let  it  descend  through  some  machine 
recipient  of  water-power,  we  have  the  tide-mill,  the  power  of 
*  Communicated  by  the  Author. 


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of  the  Earth's  Rotation.  89 

which  is  as  directly  derived  from  gravitation  as  is  that  of  a 
water-mill  upon  a  mountaia-streara.  The  water  is  raised  in  the 
former  case  by  gravitation  towai*ds  the  moon  and  by  gravitation 
falls  back  towards  the  earth ;  iu  the  latter  it  is  raised  by  evapo- 
ration^ and  falls  back  to  the  sea  by  gravitation.  It  is  true  that 
the  earth^s  and  the  moon's  rotation  are  '^  inseparable  accidents '' 
to  the  rise  and  then  the  fall  of  the  surface  of  the  sea  at  any 
particular  point;  but  the  source  of  the  power  is  derived,  not 
from  the  mechanism  nor  at  the  expense  "of  the  earth's  rotation/' 
but  as  directly  from  gravitation  as  is  the  case  in  any  ordinary 
mill-stream.  If  I  am  wrong  in  this  I  shall  gladly  accept  cor- 
rection. My  chief  object  here,  however,  is  to  ask  whether 
(assuming  the  actuality  of  retardation  of  rotation  by  the  tidal 
wave  acting  as  a  brake,  and  be  its  amount  more  or  less)  there 
may  not  be  other  forces  in  action  upon  our  globe  tending  to 
countervail  this  to  a  greater  or  less  extent.  It  seems  to  me  that 
there  arc — though,  so  far  as  my  reading  goes,  I  have  not  seen 
-any  notice  of  such  on  the  part  of  physical  writers.  Every  particle 
of  matter  (rotating  as  part  of  our  earth)  which  descends  from  a 
higher  to  a  lower  elevation,  must  in  doing  so  part  with  kinetic 
energy  proportionate  to  its  decrease  in  velocity  of  rotation  between 
its  higher  and  its  lower  positions,  and  the  energy  so  lost  is  trans- 
ferred at  the  lower  point  to  the  earth  itself.  Every  drop  of  water, 
therefore,  every  flake  of  snow  that  precipitates  upon  the  higher 
parts  of  our  globe,  if  assumed  to  reach  these  points  without 
relative  velocity,  must  in  descending  to  the  sea-level  tend  to 
accelerate  the  earth's  rotation.  So  also  every  block  of  ice  or  of 
stone  that  descends  from  the  mountain-tops,  every  particle  of 
detritus  carried  along  from  higher  levels  towards  the  sea,  must 
have  the  same  effect.  With  regard  to  the  first  it  may  be  said, 
every  particle  of  water  raised  by  evaporation  from  the  surface  of 
the  ocean  ascends  into  the  atmosphere  with  only  a  velocity  of 
eastward  rotation  due  to  the  earth's  radius  at  the  sea-level,  and 
at  the  latitude  at  which  it  is  taken  up,  and  that  therefore  when 
precipitated  upon  some  much  higher  level  it  takes  away  from 
the  earth  as  much  kinetic  energy  as  it  returns  to  it  in  descending 
in  streams  again  to  the  sea-level.  But  is  this  so?  What 
actually  passes  when  a  particle  of  sea-water  at  the  surface  of 
the  ocean,  parting  with  its  salt,  rises  therefrom  under  the  in- 
fluence of  the  sun's  heat,  and  becomes  an  invisible  vapour 
held  in  suspension  by  the  air,  is  to  a  great  extent  still  un- 
known. The  particle  of  water,  whatever  be  its  physical  con- 
dition on  leaving  the  liquid  surface,  undoubtedly  only  possesses 
the  velocity  due  to  its  low  position  upon  the  earth's  surface ; 
before  it  has  risen  even  a  fraction  of  an  inch,  however,  it  is  taken 
possession  of  by  the  air  (that  is  to  say,  by  the  winds) ;  and  all  its 


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40  On  the  Tidal  Retardation  of  the  Earth's  Rotation. 

subsequent  movemeDts  are  coerced  by  them.  Except  througa 
the  winds  it  has  no  point  d^appui  upon  the  solid  earth.  Now 
the  movements  of  the  winds,  however  largely  modified  by  the 
form  and  rotation  of  our  earth,  mainly  depend  upon  differences 
of  temperature  produced  by  the  sun's  heat ;  it  would  seem  there- 
fore that,  so  far  as  the  kinetic  energy  of  the  ascending  particle 
of  vapour  is  concerned,  it  may  or  may  not  affect,  and,  if  at 
all,  very  slightly,  the  horizontal  motions  of  the  winds,  but  can 
have  no  effect  upon  the  rotation  of  the  earth. 

The  case  is  different,  however,  as  soon  as  the  particle  of  vapour 
raised  by  molecular  forces  to  the  level  of  a  mountain-top  is  pre- 
cipitated thereon  as  rain  or  snow,  and  begins  to  desceod  again 
towards  the  ocean  whence  it  came :  at  every  foot  of  its  descent 
it  parts  with  kinetic  energy,  which  it  transfers  directly  to  the 
earth  as  a  whole.  On  the  other  hand,  such  particles  of  vapour 
as  assumed  the  form  of  rain  or  snow  at  greater  or  less  elevations, 
and  fall  directly  as  rain^drops  to  the  sea-level,  can  produce  no 
effect  in  accelerating  the  earth's  rotation,  each  drop  being  co- 
erced in  its  movements  until  within  a  short  distance  of  the  earth 
by  the  winds — that  is,  by  the  same  molecular  forces  which  raised 
them  up. 

If  this  speculation  be  admissible,  then  we  have  a  source  of 
sensible  acceleration  to  the  earth's  rotation  in  the  vast  volume  of 
water  which  is  precipitated  upon  the  dry  land  and  runs  off  into 
the  ocean.  Adopting  Gardner's  estimate  of  the  surface  of  the 
land,  exclusive  of  the  antarctic  continent,  and  assuming  a  mean 
annual  rainfall  for  the  whole  earth  of  60  inches  per  annum,  and 
that  two  thirds  of  the  entire  rainfall  returns  to  the  ocean  by 
streams  and  rivers,  we  have  23,891  cubic  miles  of  water  annually 
precipitated  and  fiEJling  back  into  the  ocean ;  and  assuming  the 
mean  height  of  the  land  to  be  about  1000  feet,  this  immense  mass, 
on  reaching  the  ocean,  has  lost  kinetic  energy  due  to  the  difference 
in  velocity  of  rotation  between  the  earth's  mean  radius  at  the 
sea-level  and  the  same  plus  1000  feet,  the  portion  of  this  which 
is  effective  in  producing  acceleration  depending  upon  the  cosine 
of  the  latitude. 

As  respects  the  descent  of  solids  from  higher  to  lower  levels^ 
there  seems  no  room  for  doubt  as  to  their  tendency  to  produce 
acceleration  in  the  earth's  rotation.  It  is  true  that  at  remote 
epochs,  when  continents  and  mountains  were  originally  ele- 
vated, their  uplifting  tended  to  retard  the  earth's  rotation,  and 
that  their  complete  ablation  could  do  no  more  than  restore  the 
energy  of  rotation  the  earth  had  before  their  upheaval.  But 
the  ocean- bed  was  depressed ;  and  its  area  is  four  times  that  of 
the  land,  and  its  mean  depth  probably  greater  than  the  mean 
height  of  the  continents ;  if,  therefore,  we  assume  the  present 


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On  some  points  in  Mallet's  Theory  of  Vulcanicity.         41 

ocean-level  as  a  datum  plane^  the  changes  of  level  originating 
land  and  sea  may  have  tended  rather  to  accelerate  than  retard 
the  earth's  rotation.  Taking  the  mean  of  the  sediment  stated 
to  be  carried  by  six  great  rivers,  namely  the  Mississippi,  Po, 
Vistula,  Rhine,  Ganges,  and  Rhone,  it  amounts  to  about  y^Vir 
in  volume  of  the  water  discharged ;  and  if  we  apply  this  to  the 
water  discharged  from  the  whole  surface  of  the  land,  as  above 
stated,  we  have  -8j^^^=  19*90  cubic  miles  of  sediment  annually 
discharged  at  the  sea-level.  These  rough  estimates  are  pro- 
bably far  from  correct,  and  we  do  not  know  with  any  pre- 
cision what  is  the  mean  specific  gravity  of  this  sediment,  nor 
from  what  mean  height  it  may  be  considered  to  have  descended ; 
but  we  can  easily  see  that  the  loss  of  rotative  energy  during  the 
descent  of  this  vast  mass,  if  transferred  to  the  globe  as  a  whole, 
is  scarcely  negligible.  Nor  does  this  represent  all  that  we  have 
to  deal  with.  The  sediment  finally  carried  into  the  sea  repre- 
sents the  real  annual  degradation  of  the  land  by  rain  and  rivers ; 
and  the  huge  block  that  falls  to-day  from  a  Sierra  summit  and 
wedges  itself  a  few  miles  off  immovably  in  the  cleft  of  a  canon, 
though  it  may  not  reach  the  sea  for  thousands  of  years,  daring 
which  it  is  slowly  transformed  into  sediment,  is  nevertheless 
effective,  as  is  the  ice  which  thaws  or  falls  in  avsJanche,  in  trans- 
ferring to  our  earth  the  energy  of  rotation  they  lose  in  descent. 
Whether  or  not  it  be  true  that,  viewed  on  its  largest  scale  and 
at  some  indefinitely  remote  period  yet  to  come,  the  movements 
of  all  the  bodies  of  the  universe  tend  to  ultimate  rest,  and  an 
end  of  the  present  order  of  things,  it  seems  a  fact  that  all  the 
smaller  perturbations  of  planetary  movement  at  least,  as  for 
example  those  of  precession  and  nutation,  are  involved  in  con- 
ditions which  prevent  their  passing  a  certain  limit,  and  which  in 
other  cases  equilibrate  the  disturbing  cause.  It  would  seem, 
therefore,  contrary  to  analogy  to  suppose  the  case  of  the  retar- 
dation of  our  globe  by  tidal  friction,  whatever  niay  be  its  actual 
amount,  to  be  an  exception  and  to  go  on  unchecked,  until  the 
astronomical  consequences  pointed  out  by  Thomson  and  others 
shall  have  occurred  in  the  motions  of  our  satellite,  our  earth, 
and  the  sun. 


VI.  On  some  points  in  Mallet's  Theory  of  Vulcanicity, 
By  EuG.  W.  HiLGAKO,  University  of  Michigan** 

THE  main  points  of  Mallet's  Theory  of  Vulcanicity  have 
been  before  the  world  of  science  for  some  time,  and  have 
excited  some  lively  discussions  on  both  sides  of  the  question, 

*  From  Silliman's  American  Journal^  June  18/4. 


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42  Mr.  E.  W.  Hilgard  on  some  points  in 

mainly  in  the  English  press.  I  think  it  is  to  be  greatly  regretted 
that  the  original  memoir,  very  tardily  published  in  the  Transac- 
tions of  the  Royal  Society,  should  be  so  difficult  of  access,  that 
few  of  those  interested  are  enabled  to  appreciate  the  caution  and 
laborious  conscientiousness  which  Mallet  has  brought  to  bear  on 
his  investigation  and  discussion  of  this  most  complex  problem^ 
and  to  what  extent  he  has  himself  anticipated  most  of  the  ob- 
jections raised.  In  calling  attention  to  some  apparent  omissions 
in  this  respect,  it  may  be  useful  to  recall  the  state  of  the  ques- 
tion as  regards  some  of  the  more  prominent  points  at  issue. 

The  first  and  most  sweeping  attack  upon  the  very  basts  of 
Mallet^s  theory  comes  from  Sir  William  Thomson,  in  a  letter  to 
Mr.  Poulett  Scrope  (Nature,  Feb.  1,  1872),  in  which  he  calls 
attention  to,  and  reaffirms  the  results  of  his  investigation  (supple- 
mentary to  that  of  Hopkins)  on  the  effect  which  a  fluid  nucleus 
and  imperfect  rigidity  of  the  earth  must  exert  upon  precession 
and  nutation,  and  which  led  him  to  the  conclusion  that,  unless 
the  rigidity  of  the  globe  as  a  whole  were  greater  than  that  of 
steel,  there  must  ensue  a  tidal  deformation  of  the  solid  mass, 
which  would  sensibly  change  the  amount  of  precession.  He 
denies  that  Delaunay  has  shaken,  in  any  important  point,  the 
conclusions  of  Hopkins  or  himself. 

The  subject  has  since  been  taken  up  by  General  Bumard 
(Smithes  Contr.  No.  240),  who,  while  confirming  the  results  of 
Thomson  upon  the  premises  assumed  by  that  physicist,  also 
shows  that  there  are  assumable  and  admissible  conoitions  upon 
which  a  fluid  nucleus  with  a  moderately  thick  crust  may  exhibit 
the  same  constant,  or  periodically  recurrent,  amounts  of  preces- 
sion and  nutation  as  a  solid  globe. 

Mallet  refers  to  Thomson's  argument  in  favour  of  great  rigi- 
dity as  corroborative  of  the  necessity  for  assuming  a  crust  of 
great  thickness^  such  as  would  render  it  inadmissible  to  assume 
a  direct  connexion  between  volcanoes  and  the  liquid  nucleus. 
But  it  is  difficult  to  see  how  the  ''  preternatural  rigidity,'^  made 
a  postulate  by  Thomson,  could  in  any  manner  be  compatible 
with  the  requirements  of  Mallet's  theory.  For  the  latter  repre- 
sents the  earth's  crust  as  a  congeries  of  fragments^  sustained 
partly  by  the  contracting  liquid  nucleus,  partly  by  each  other 
on  the  principle  of  the  arch — therefore  necessarily  often  locally 
in  a  state  of  unstable  equilibrium,  and  liable  to  be  disturbed 
by  slight  outside  forces.  That  the  tendency  to  tidal  deforma- 
tion contributes  toward  producing  such  disturbances  has  been 
rendered  probable  by  Perrey's  discussions,  and  by  the  repeated 
coincidence  of  violent  earthquakes  with  tiual  extremes,  lately 
observed. 

Thomson's  assumption,  that  the  postulated  rigidity  might 


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Mallet's  Tl^eory  of  Vulcanieity.  43 

result  from  compression,  would  scarcely  seem  admissible,  save  in 
a  case  of  absolute  homogeneity  and  equilibrium — if  then.  It  is 
certainly  incompatible  with  the  demonstration  made  by  Professor 
Belli  of  Favia  (as  quoted  by  Mallet),  to  the  effect  that  rigid 
bodies  are  weakened  by  the  simultaneous  application  of  ortho- 
gonal pressures — that  no  known  materials  could  sustain,  under 
any  circumstances,  a  strain  several  hundred  times  greater  than 
that  which  would  crush  it  if  laterally  free  to  yield — ^that  such 
strains  exist  in  the  contracting  crust,  and  that  upward  deforma- 
tion must  result,  if  such  contraction  takes  place  at  all,  as  the 
annual  loss  of  heat  by  the  earth  compels  us  to  assume  is  the  case. 

Whether  we  view  the  question  of  rigidity  by  the  light  of  our 
direct  knowledge  of  the  first  twenty- five  miles  of  crust,  and  of 
the  profound  commotions  it  experiences  from  time  to  time,  or 
by  that  of  the  demonstrated  increase  of  temperature  as  we  de- 
scend, rendering  it  extremely  probable  that  at  a  comparatively 
slight  depth  the  rigidity  of  all  materials  must  be  seriously  im- 
paired by  a  high  temperature  despite  of  pressure — or  whether 
we  even  consider  alone  the  secular  loss  of  heat  by  radiation, 
which  must  result  in  a  contraction  affecting  unequally  the  hete- 
rogeneous couches  of  which,  on  any  hypothesis,  the  solid  portion 
of  the  earth  must  be  composed — it  will  be  difficult  to  persuade 
geologists  of  the  actual  existence  of  the  '^  preternatural  rigidity '' 
until  every  reasonable  hypothesis  that  can  dispense  with  this 
assumption  shall  have  been  exhausted. 

Among  the  objections  raised  by  geologists,  the  first,  and  ap- 
parently gravest,  was  that  of  Forbes  (Nature,  Feb.  6,  1872), 
who  argues  the  untenableness  of  Mallet's  theory  on  the  ground 
of  the  asserted  general  identity  of  composition  of  volcanic 
ejecta.  In  fact,  from  Mallet's  point  of  view,  it  would  seem  that 
lavas  might  have  the  composition  of  any  fusible  rock  whatso- 
ever in  whose  strata  the  crushing  might  happen  to  occur,  and 
hence  that,  if  taking  place  within  the  sedimentary  strata,  there 
ought  to  be  a  very  great  diversity  between  the  ejecta  of  different 
vents. 

In  his  rejoinder  Mallet  calls  attention  to  the  very  serious  dif- 
ferences of  composition  between  the  extremes  of  trachytic  and 
basaltic  lavas,  and  to  the  generally  admitted  fact  that  volcanoes 
are  located  along  axes  of  upheaval,  where  the  hypogene  rocks, 
and  therefore  those  of  the  crust  proper,  approach  the  sur- 
face— hence  that  crushing  along  these  lines  of  weakness  would 
be  by  no  means  likely  to  produce  a  greater  diversity  of  lavas 
than  we  actually  observe.  Furthermore,  that  the  ^'  local  lake  " 
theory  is  liable  to  the  same  objection,  unless  the  lakes  are  sup- 
posed to  be  located  within  the  (uniform)  crust  itself. 

He  might,  it  seems  to  me,  have  added  that  the  maximum  of 


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44  Mr.  E.  W.  Hilgard  on  some  points  in 

twenty-five  miles  of  sedimentary  rocks  is  not  anywhere  (on  the 
continental  areas  at  least)  actually  superimposed  vertically  upon 
the  crusty  and  hence  that  it  is  not  unreasonable  to  assume 
that  a  pressure  sufficiently  great  to  produce  fusion  may  never 
occur  within  the  limits  of  the  sedimentary  strata^  albeit  other 
manifestations  of  subterraneous  thermal  action  may  not  be 
wanting.  It  is  true  that^  on  the  whole,  Mallet's  memoir  leaves 
upon  the  reader's  mind  the  impression  that  he  seeks  the  source 
of  volcanic  action  at  depths  sufficiently  shallow  to  justify  in  a 
measure  the  objection  raised  by  Forbes,  although  he  ex- 
pressly declares  that,  with  our  present  data,  the  determination 
of  the  points  at  which  the  maximum  of  crushing-effects  occurs 
is  impossible. 

Similar  considerations  apply  to  the  objection  raised  by  P.  W. 
Button  (Nature,  Nov.  27, 1873),  that  *Maults  show  no  heating- 
effects,  even  where  considerable  crushing  has  taken  place.'' 
The  pressure  under  which  the  faulting  occurred  may  have  been 
inadequate,  in  the  cases  coming  under  our  observation;  but 
above  all,  time  is  a  most  essential  element  in  this  connexion. 
No  matter  how  great  the  dislocation  or  crushing,  no  great  in- 
crease  of  temperature  can  occur  if  it  takes  place  slowly ,  however 
great  may  be  the  quantity  of  work  performed,  or  of  heat  pro- 
duced. And  very  many,  if  not  the  majority  of  extensive  faults 
actually  occurring,  show  evidence  of  having  been  formed  without 
cataclysmal  disturbance. 

Among  the  other  points  raised  by  Hutton  {loc.  cit.)  there  are 
several  which  are  at  once  disposed  of  by  a  perusal  of  the  original 
memoir.  There  are  others  of  some  weight.  That  ^' lines  of 
least  resistance  once  chosen  must  remain,"  is  doubtless  true  in 
a  very  wide  sense ;  and  in  that  sense  this  is  scarcely  at  variance 
with  observed  facts,  since  the  lines  of  weakness  along  the  bor- 
ders of  continents  are  still  those  which  exhibit  volcanic  activity 
(and  earthquake  phenomena)  most  frequently.  But  in  the  fold- 
ing and  upheaving  of  strata  by  tangential  thrust  the  question 
of  equilibrium  must  often*of  necessity  be  very  delicately  balanced, 
depending  as  it  does  upon  the  vertical  pressure  of  the  masses^ 
their  nature,  dislocation,  subsequent  consolidation,  igneous 
effusions  from  iissures,  &c.  Lines  of  weakness  as  to  rigidity 
may  thus  easily  acquire  sufficient  static  resistance  to  cause  a 
subsequent  yielding  to  take  place  at  some  distance  from  the 
original  axis,  as  is  exemplified  in  the  formation  of  successive 
parallel  ranges.  What  is  true  with  regard  to  the  formation  of 
folds  is  equally  so  as  concerns  the  settling  down  of  the  crust- 
fragments  in  consequence  of  interior  contraction.  Each  frag- 
ment as  a  whole  may  remain  as  such,  being  only,  as  it  were, 
abraded  at  its  circumference.     But  it  is  only  necessary  to  have 


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Mallet^s  Theory  of  Vulcanicity.  46 

observed  the  gradual  yielding  of  detrital  rock-masses  under  pres- 
sure^ to  understand  why  the  cataelysmal  yielding  which  mani- 
fests itself  in  earthquakes  should  so  frequently  change  its  locality 
of  occurrence — why  for  long  periods  a  region  may  be  completely 
exempt  from  these  movements^  in  consequence  either  of  an  un- 
resisted and  therefore  gradual  descent  of  the  crust-fragments 
underlying  it,  or  of  an  arch-like  arrangement,  whose  sudden 
breaking  down  will  result  in  a  catastrophe,  succeeded  perhaps 
by  a  long  period  of  quiescence. 

Thus  Mallet^s  theory  accounts  equally  well  for  the  sporadic 
and  apparently  lawless  occurrence  of  seismic  phenomena,  and 
for  the  probable  correlation  between  the  frequency  and  violence 
of  earthquakes  and  tidal  extremes.  Unlike  the  theory  of  a  thin 
crust,  which  would  lead  us  to  expect  almost  diurnal  earthquakes 
corresponding  to  oceanic  tides,  according  to  Mallet's  view  there 
should  be  a  near  coincidence  in  time  and  space  of  two  indepen* 
dent  factors  (viz.  of  a  condition  of  very  unstable  equilibrium  of 
some  crust-fragment,  with  a  tidal  extreme)  in  order  to  produce 
a  maximum  of  disturbance.  It  cannot  be  expected  that  such 
coincidence  should  be  of  frequent  occurrence,  or  that  the  casual 
connexion  should  manifest  itself  in  a  greater  predominance  than 
that  claimed  by  Perrey  for  the  times  of  spring  and  neap  tides. 
Mallet  does  not,  however,  allude  to  this  point — whether  from  a 
distrust  of  Perrey's  data  and  method,  or  theoretical  scruples  on 
the  score  of  "  rigidity .'' 

The  objection,  that  according  to  Mallet's  theory  earthquake;?} 
ought  always  to  be  followed  by  eruptions,  could  obviously 
apply  only  during  the  period  of  fissure  eruptions  from  the 
liquid  interior — it  being  conceded  that  the  volcanic  eruptions 
of  to-day  are  due  to  contact  of  water  with  the  molten  rock,  and 
that  steam,  not  static  pressure,  is  the  vis  a  tergo.  It  is,  of 
course,  very  probable  that  the  access  of  water  to  the  volcanic 
focus*  is  generally  caused  or  facilitated  by  such  crust-move- 
ments as  would  at  the  same  time  result  in  the  production  of 
more  heat  and  perhaps  of  fused  rock,  such  movements  being 
indicated  by  the  (mostly  slight)  earthquakes  that  so  frequently 
precede  a  period  of  volcanic  activity.  Hutton's  objection,  that 
according  to  Mallet's  view  each  eruption  ought  to  be  preceded 
by  a  sensible  subsidence,  is  therefore  groundless. 

One  point,  however,  must  strike  every  reader  of  the  original 
memoir,  viz.  the  preeminence  given  by  Mallet  to  the  crushing  of 
solid  rock  as  the  means  of  producing  heat  and  fusion.  Que 
would  naturally  look  to  the  results  of  his  experiments  on  this 

♦  Hut  ton  {loc.  cit,)  avers  that  "  to  cause  a  volcano  the  heat  must  go  to 
the  water ;  the  water  cannot  go  to  the  heat>"  but  omits  any  explanation  of 
this  singular  axiom. 


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46  Mr.  E.  W.  Hilgard  on  some  points  in 

subject  for  the  proof  of  the  efficiency  of  this  agency.  But  we 
find  that  the  maximum  of  temperature  resulting  from  the  crush- 
ing to  powder*  of  the  hardest  rock  is  something  over  217^ 
Fahr.  This,  then,  represents  the  maximum  increment  of  tem- 
perature that  can  be  rendered  efficient  toward  the  fusing  of 
rocks  by  the  crushing  process  under  the  most  favourable  cir- 
cumstances, viz.  upon  the  supposition  that  it  takes  place  in- 
stantaneously, or  under  such  circumstances  that  the  heat  can- 
uot  be  conducted  away,  and,  further,  that  the  resistance  of  the 
rock  has  not  been  materially  diminished  by  the  downward  in- 
crease of  hypogeal  temperature.  At  the  most  moderate  depths 
at  which  volcanic  phenomena  can  be  supposed  to  originate,  the 
last-mentioned  factor  must  exert  a  very  considerable  influence, 
reducing  mateiially  the  available  heat-increment.  Hence  the 
numerical  results  of  Mallet's  laborious  experiments  on  rock- 
crushing,  however  interesting  and  useful  as  affording  a  definite 
measure  of  the  thermal  effects  producible  by  this  means,  yet 
fail  to  carry  conviction  as  to  the  efficacy  of  this  particular  modus 
operandi  in  reducing  large  masses  of  solid  rock  to  fusion,  unless 
essentially  supplemented  by  friction,  not  so  much  of  rock  walls 
against  each  other,  but  more  probably  by  the  heat  produced 
within  more  or  less  comminuted  detrital  or  igneoplastic  masses 
by  violent  pi'essure  and  deformation. 

It  may  be  doubtful  what  would  be  the  physical  and  thermal 
effect  of  enormously  great  pressures  upon  rock  powder  such  as 
was  produced  in  Mallet's  experiments ;  but  it  would  seem  that 
if  made  to  yield,  the  frictional  effect  must  produce  very  high 
temperatures.  A  fortiori,  solid  detrital  masses  of  variously 
sized  fragments  intermingled  (such  as,  rather  than  powder, 
would  be  likely  to  result  from  steady  pressure),  yielding  rapidly 
under  great  pressures,  might,  under  the  combined  influence  of 
friction  and  rock-crushing,  well  be  supposed  to  reach  the  tempe- 
rature of  fusion,  which  a  simple  crushing  of  a  solid  mass  by 
pressure  would  have  failed  to  produce.  Mallet  mentions  the 
probable  influence  of  friction,  and  of  the  squeezing  of  igneo- 
plastic masses,  but  does  not  attach  to  these  agencies  such  im- 
portance as  they  seem  to  me  to  deserve. 

Of  the  complex  thermal  effects  of  the  movements  of  detrital 
masses  under  great  pressure.  Mallet's  figures  of  course  offer  no 
measure  whatsoever ;  nor  is  this,  or  even  the  thermal  coefficients 
resulting  from  his  rock- crushing  experiments,  at  all  necessary 
to  the  establishment  of  the  postulates  of  his  theory. 

*  Mallet  does  not  go  into  the  consideration  of  the  physical  nature  of  this 
"  powder,"  and  of  the  thermal  and  other  differences  likely  to  result  from 
its  production  under  pressures  enormously  greater  than  those  employed 
by  him. 


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Mallet's  Theory  of  Vtdcamcity.  47 

Taking  for  granted  the  correctness  of  Hirn's  theorem,  '^  that 
the  heat  evolved  in  the  crushing  of  rigid  bodies  is  the  equiva- 
lent of  the  work  performed/'  Mallet's  experiments  on  the  con- 
traction of  fused  rock  in  cooling,  and  his  estimates  of  the  amount 
of  volcanic  energy  manifested  on  the  globe,  coupled  with  that  of 
the  earth's  annual  loss  of  heat,  completed  the  proof  of  the  qimu' 
titative  adequacy  of  the  cause  invoked  by  him.  And  when  it  is 
understood  that  the  earth's  present  loss  of  heat  during  sixteen 
and  a  half  years  is  the  mechanical  equivalent  of  all  the  volcanic 
work  performed  since  the  period  of  fissure  eruptions,  the  burthen 
of  proof  of  the  qualitative  inefficiency  of  the  several  modes  of 
action  that  may  come  into  play  would  seem  to  be  effectually 
thrown  upon  the  opponents  of  the  theory. 

Among  these  modes  of  action,  the  fusion  of  masses  already 
existing  in  a  pasty,  or  generally  more  or  less  igneoplastic  con- 
dition, by  squeezing  or  forcible  displacement,  seems  to  me  to 
deserve  especial  attention.  At  the  depth  at  which  volcanic 
phenomena  must  be  supposed  to  originate,  this  condition  must 
be  closely  approached,  especially  in  the  early  times  of  the  vol- 
eanic  period — that  of  the  '^  Maare  "  of  the  Eifel  and  other  simi- 
lar cases  representing  the  transition  phase  between  the  regime 
of  fissure-eruptions  and  that  of  volcanoes  proper.  In  this 
period  of  a  ^  greatly  stiffened  and  thickened  crust,''  even  slight 
flexures,  whether  synclinal  or  anticlinal,  would  occasion  great 
displacements  and  movements  in  the  half-stiffened  upper  layers 
of  the  "viscous  couchc/'  and  if  these  experienced  local  re- 
fusion, the  fused  matter  may  well  be  presumed  to  have  often 
been  disposed  of  by  eruption  through  fissures  or  volcanic  vents, 
rather  than  by  overcoming  downward  the  inertia  of  the  viscous 
couches*  This  mode  of  action  seems  to  me  likely  not  only  to 
afford  a  more  copious,  but  also  a  more  constant  or  lasting  source 
of  supply  than  the  supposed  crushing  of  solid  rock,  and  appears 
especially  applicable  to  the  case  of  large  fissure-eruptions. 

Among  the  greatest  services  rendered  by  Mallet's  (or,  in  this 
connexion,  Wurtz's)  theory  is  the  unstrained  explanation  of 
many  of  the  phenomena  of  mctamorphism  that  were  quite  un- 
intelligible so  long  as  the  heat  required  for  the  observed 
changes  was  supposed  to  be  derived  from  below,  and  perhaps 
by  transmission  through  strata  which  themselves  bad  experi- 
enced little  or  no  change  of  condition.  The  principle  that  the 
heat  evolved  in  the  flexure  or  forcible  compression  of  strata  is, 
cateris  paribus,  proportional  to  the  resistance  offered  by  them 
to  the  external  force,  throws  a  flood  of  light  upon  numerous 
apparently  contradictory  phenomena,  which  have  long  been 
quoted  as  incompatible  with  the  doctriue  of  metamorphism  as 
held  in  this  country,  and  have  stood  in  the  way  of  its  general 


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48  Mr.  £•  W.  Hilgard  on  some  points  in 

acceptance  by  geologists,  particularly  on  the  continent  of 
Europe.  In  its  application  to  the  formation  of  synclinoria 
especially,  the  principle  works  most  instructively  and  satisfac- 
torily. It  can  scarcely  be  doubted  that  in  the  first  folding  of 
the  vertex  of  a  geosynclinal^  weakened  below  by  fusing  away 
and  heating  of  the  crust  and  lowest  strata,  the  movements 
were  comparatively  localized  and  rapid,  and  therefore  capable 
of  producing  high  temperatures,  and  their  results  such  as  we 
now  usually  find  them  along  the  main  axes  of  elevation  of  syn- 
clinoria.  But  as  the  resistance  along  this  axis  increased  by 
emergence  and  solidification,  the  points  of  yielding  (t.  e,  the 
folds)  would  be  muli^lied,  while  the  absolute  amount  of  motion 
transformable  into  heat  would  be  diminished  in  each.  Hence 
the  decrease  in  general  of  metamorphic  effects  as  we  recede 
from  the  main  axis.  And  yet  it  is  perfectly  easy  to  conceive 
of  large  local  exceptions  to  the  general  rule  (such  as  we  actu- 
ally observe),  on  the  basis  of  greater  resistance  in  perhaps  a 
localized  stratum  of  a  lateral  fold,  yet  so  situated  that  it  could 
not  successfully  resist  the  influence  of  an  advantage  of  leverage 
causing  a  rapid  deformation.  It  is  even  predicable  that  under 
such  circumstances  sudden  breaks  and  crushings  must  occa- 
sionally have  occurred,  giving  rise  to  fusion  of  rocks  and  limited 
fissure-eruptions,  or  at  least  to  pasty  rock  intrusions — as  sug- 
gested by  Dana  for  granitic  and  analogous  veins^  that  show  no 
evidences  of  the  cooperation  of  very  high  temperature  in  the 
act  of  formation. 

LeConte's  view,  that  the  first  mashing  of  a  geosynclinal 
would  produce  less  heat  than  later  plications*,  in  which  (pre- 
sumably) a  greater  resistance  would  have  to  be  overcome,  seems 
hardly  to  be  compatible  with  facts  as  generally  observed  away 
from  the  Pacific-coast  eruptions ;  and  his  argument  is  the  less 
cogent,  as  the  temperature  produced  is  a  function,  not  only  of 
the  resistance  of  the  rocks,  but  also  of  the  degree  and  rapidity 
of  the  motions,  both  of  which  have  been  on  the  decrease  in  late 
geological  periods^  in  accordance  with  the  diminishing  rate  of 
contraction  of  the  earth  and  the  increased  resistance  of  the  crust 
to  flexure. 

While  Mallet's  theory  accounts  satisfactorily  for  earthquake 
phenomena  and  volcanic  activity  as  manifested  since  the  cessa- 
tion of  fissure-eruptions,  and  also  for  the  gradual  or  sudden 
depression  of  both  large  and  small  areas  even  subsequent  to 
that  time,  it  makes  no  provision  for  their  elevation,  and  there- 
fore leaves  unexplained  the  numerous  oscillations  of  level  of 
which  we  find  the  record  down  to  our  own  time.     In  assuming 

*  "  On  the  great  Lava-flood  of  the  West«'*  Silliman's  American  Journal, 
March  1874,  p.  179. 


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Mallet's  Theory  ofVukanieity.  49 

the  movements  as  taking  place  exclusively  within  the  solid 
shell,  he  (unnecessarily  as  it  seems  to  me)  leaves  a  point  open 
to  obiection. 

While  admitting  that  slow  secular  oscillations,  or  those  minor 
changes  of  level  constantly  occurring  in  volcanic  areas,  may 
even  now  in  many  cases  be  reasonably  attributed  to  changes  of 
temperature  occurring  within  the  solid  rocks  themselves,  and 
within  their  limits  of  elasticity,  it  is  impossible  to  assign  this 
as  an  adequate  cause  of  those  extensive  oscillations  which 
have  characterised  the  Quaternary  period,  and  are  recorded, 
€.  g.y  by  the  raised  beaches  of  the  North-Atlantic  coasts  and 
inlets,  and  by  the  drift-pebbles  even  now  found  four  hundred 
and  fifty  feet  below  the  level  of  the  Gulf  of  Mexico,  while  the 
emerged  formations  record  a  complementary  elevation  to  at 
least  a  similar  extent  during  the  Terrace  epoch.  This  record 
of  an  oscillation  of  near  a  thousand  feet  on  the  Gulf-shore 
since  the  glacial-drift  epoch,  implies  at  least  a  corresponding  one 
over  the  greater  portion  of  the  area  drained  by  the  Mississippi, 
unless  that  river  flowed  backward  at  one  time*.  Doubtless 
these  oscillations,  like  the  glaciation  of  which  they  probably 
were  cooperative  causes,  were  of  continental  extent,  as  was  the 
(more  or  less  contemporary)  emergence  of  the  Siberian  plain ; 
and  as  such  they  must  be  presumed  to  have  been  true  move- 
ments of  the  earth's  crust,  although  lying  quite  within  the  vol- 
canic period  proper.  It  is  but  reasonable  to  suppose  that  the 
sinking  of  the  great  Pacific  area  was  then,  and  may  still  be, 
of  a  similar  nature. 

If  Mallet's  theory,  as  well  as  the  geological  facts  with  which 
it  deals,  is  incompatible  with  Hopkins's  and  Thomson's  postu- 
late of  extreme  rigidity ;  if,  as  it  appears  to  me,  the  events  of 
very  recent  geological  epochs  in  connexion  with  the  very  slow 
rate  of  cooling  since  that  time  render  it  unlikely  that  the  crust 
can  even  now  be  considered  rigid  in  a  geological  sense;  if^ 
finally,  as  General  Barnard  affirms,  the  astronomical  objection  to 
a  comparatively  pliant  crust  and  liquid  nucleus  is  not  absolute, 

*  It  is  a  cunous  fact  that  in  the  vaiious  hv  pothenes  regarding  the  oscil- 
lations of  the  continental  interior  during  tlie  Drift  epoch,  the  facts  ob- 
served on  the  Gulf-shore  have  over  and  again  been  quietly  ignored, 
although  the  Gulf  is  unequivocally  the  natural  reference-level  most  directly 
related  to  that  interior,  not  only  at  the  present  time,  but;  as  the  direction 
of  the  Drift  currents  and  the  trend  of  the  formations  show,  ever  since  the 
time  of  the  Cretaceous  emergence.  Nevertheless  the  reference- level  has 
been  sought  bevond  the  Alleghany  upheavals,  or  beyond  the  fixed  Azoic 
area  upon  which  the  movement  appears,  in  a  measure,  to  have  pivoted, 
and  wnere,  as  Dana  has  shown,  it  was  materially  diminished  in  extent. 
Assuredly  no  hypothesis  which  disregards  the  changes  of  level  registered 
at  the  continental  outlet  has  any  raison  (Petre ! 

PhU.  Mag.  S.  4.  Vol.  48.  No.  315.  July  1874.  E 


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50  Mr.  B.  W.  Hilgard  on  some  points  in 

but  may  be  obviated  by  admissible  assumptions  regarding  the 
mode  of  distribution  of  the  solid  and  liquid  matter  constituting 
the  globe^ — ^we  are  led  to  the  reasonable  assumption  that  while 
the  thickness  and  rigidity  of  the  crust  is  evidently  too  great  to 
admit  of  further  folding  or  fissure-eruptions^  and  (probably)  to 
admit  of  connecting  ordinary  volcanic  phenomena  directly  with 
the  (virtually  or  actually)  liquid  interior^  yet  we  need  not  as- 
sume it  to  be  so  great  as  to  render  the  crust  incapable  of  yield- 
ing somewhat^  on  a  large  scale,  to  static  upward  pressure.  Such 
pressure  may  be  either  the  resultant  of  tangential  stress^  such 
as  might  slightly  deform  an  arch  without  fracture  or  folding, 
or  even  the  direct  result  of  a  corresponding  subsidence  else- 
where. 

The  latter  effect  would  of  course  be  incompatible  with  a 
shrinking  away  of  the  fluid  interior  &om  the  crusty  as  required 
by  Mallet's  theory^  if  it  were  necessary  to  assume  that  the  in- 
terior crust-surface  is  substantially  '^  smooth/'  t.  e.  free  from 
important  downward  projections  or  upward  sinuosities.  But  so 
far  from  this,  the  cooling  influence  that  has  so  long  acted  on 
the  oceanic  areas,  contrasted  with  those  enormous  outwellings 
of  igneous  rock  that  have  occurred  even  in  late  Tertiary  or 
Posttertiary  times,  together  with  other  considerations,  necessi- 
tate the  assumption  that  such  inequalities  do  exist  to  a  notable 
extent.  Hence  the  overlapping  alluded  to  by  Mallet  of  the 
period  of  fissure-eruptions  and  of  that  of  volcanic  activity 
proper,  which  appear  to  have  coexisted,  in  different  portions  of 
the  globe,  from  early  Tertiary  to  early  Quaternary  times.  For 
even  Mallet  himself  considers  the  outpourings  of  igneous  rocks 
on  the  Pacific  coast  "wholly  inconsistent  with  existing  vol- 
canic forces/'  and  few  geologists  will  agree  with  LeConte*  in 
ascribing  precisely  these  most  extensive  fissure-eruptions  in  the 
world  to  the  "  ineffectual  fires ''  of  the  volcanic  period,  arising 
alone  from  transformed  motion. 

Indeed  it  is  not  easy  to  understand  the  precise  mechanism 
of  the  great  fissure-eruptions  as  a  consequence  of  nucleal  con- 
traction, without  the  aid  of  some  static  head  of  pressure  that  may 
exist  more  or  less  locally,  in  consequence  of  inequalities  in  the 
crust  (whether  of  form,  thicknessi  or  density),  and  thus  act  as 
Si  vis  a  tergo. 

At  first  blush  the  '' squeezing  out  of  sub-mountain  liquid 
matter,"  assumed  by  LeConte  as  the  consequence  of  the  fold- 
ing and  fissuring  of  strata  by  tangential  thrust,  appears  natural 
enough.  Yet  it  seems  hardly  possible  that  the  same  force 
which  makes  and  elevates  mountain  folds  (being  the  result  of 
interior  shrinkage)  should  at  the  same  time  serve  to  compress  the 
*  SiUiman's  American  Journal,  March  1874,  p.  1/9. 


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Malleus  Theory  of  Vuiamkiiy.  51 

wUerior  Uqwii,  xuaikm  either  sueh  folding  oeeon  benealh  tke 
g^Mral  k^  of  the  liquid,  or  the  latter  is  locally  confined, 
or  the  morement  is  so  (comparatively)  brusque  or  cataclysmal, 
that  viscosity  would  prevent  the  lateral  or  downward  escape  of 
the  liquid  rock.  In  the  case  of  the  Pacific  eruptions  the  evi- 
dence of  steady  static  outflow  and  regular  upbuilding  is  espe- 
cially eogent;  and,  as  LeConte  remarks,  it  has  been  ^ow  work, 
as  indeed  is  usually  or  universally  the  case  with  mountain* 
building'^* 

The  assumption  of  locally  limited  fire  seas  with  a  solid  globe 
as  made  by  Danaf  in  conformity  with  Hopkins's  views,  would 
remove  the  difficulty  if  the  ^rust  ocrald  be  assumed  as  contract- 
ing on  the  whole  independently  of  the  portions  over  fire  seas. 
But  when  we  come  to  discuss  the  appUcation  in  detail  of  this 
intrinsically  improbable  hypothesis,  we  find  the  required  ex- 
tent and  localities  of  these  fire  seas  to  be  such  that  we  can 
hardly  imagine  them  to  be  eflfectually  separated  from  eaeh 
other;  in  other  words,  we  approach  very  near  to  a  condition  of 
general  undercrust  fluidity  up  to  late  geological  periods  j:.  It 
then  becomes  a  question  of  minor  importance  whether  there  is 
a  central  nucleus  solidified  by  pressure,  or  whether  all  within 
the  crust  is  actually  liquid. 

The  inherent  improbability  of  the  depression  of  a  ^eosyn- 
dinal  trough  to  a  level  so  low  as  to  allow  the  liqmd  rock 
to  rise  into  t/,  as  it  were,  is  too  great  to  render  its  discussion 
necessary. 

Indeed  it  seems  almost  impossible  to  imagine  a  mechanism 
explaining  satisfactorily  fissure-eruptions  such  as  those  of  the 
Pacific  coast,  on  the  basis  of  a  slowly  contracting  9oHd  crust 
with  a  rapidly  contracting  liquid  layer  or  nucleus  beneath.  A 
more  satisfactory  explanation  seems  possible  if,  in  accordance 
with  Mallet's  suggestion  and  the  intrinsic  probabilities  of  the 

*  When  LeConte  savs  {loe,  cit,  p.  179)  that  the  outoqueezing  of  the 
liquid  hai  been  caused  by  "  enormous  horizontal  pressure,  determined  by 
the  interior  contraction  of  the  whole  earth,"  and  then  (p.  180)  that, 
^  whether  by  uplifting  or  upbuilding  the  actual  increase  of  height  would 
be  precisely  the  same,  being  detennmed  by  the  amount  of  kteral  crush- 
ing,'' he  seems  to  think  of  crust-oontrac^on  upon  a  nucleus  too  large  for 
it,  rather  than  of  Mallet's  "  freely  descending  "  crust.  Or,  if  he  considers 
the  fused  rock  the  result  of  motion  transformed,  it  is  difficult  to  see  on 
what  ground  a  simple  **  uplifting  "  could  be  considered  the  precise  mecha- 
nical equivalent  of  an  upbuilding  by  eruption  of  Uquid  rock.  In  either 
ease  the  UfHng  done  would  be  the  same ;  but  what  of  the  enormous  heat 
qffiuianl 

t  "  On  some  of  the  Results  of  the  Earth's  Contraction,"  Silliman's 
American  Journal,  August  1873,  p.  105. 

t  Ibid.  July  IB73,  p.  7  et  seqq. 

E2 


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63        On  game  pdiaU  in  Maliet's  Theory  of  VulcanieUy. 

case,  we  as^ame  the  existence  of  a  thickly  viscid/  igneoplastic 
uodercrnst  layer.  Such  a  byer,  while  barely  or  very  slowly 
obeyine  the  laws  of  li(^uid  equilibrium,  would  be  capable  of 
being  liquefied  by  a  slight  increase  of  tCDiperature,  such  as 
might  be  produced  by  squeesing  or  kneading.  Portions  of 
such  plastic  matter  would  occasionally  become  involved  in  the 
anticlinal  folds  of  syndinoria,  and  thus  supply  the  material  for 
limited  fissure-eruptions,  in  that  case  literally  '*  squeezed  out." 
But  the  inverse  ratio  pointed  out  by  Dana  as  existing  between 
folding  and  fissure-eruptions  points  to  the  rarity  of  such 
events. 

At  any  rate  they  could  not  explain  the  outwellings  of  the 
Pacific  border^  which  continued  long  after  close  plications  had 
ceased  to  be  made — in  fact,  as  it  would  seem,  up  to  the  end  of 
the  period  of  elevation  of  the  main  Sierra  Nevada. 

It  is  but  fair  to  assume  that  near  lines  of  weakness  indicated 
by  plications  or  fissure-eruptions,  the  isogeotherms  have  been 
during  the  elevation  of  mountain-chains  (and  probably  still  are 
where  such  lines  are  marked  by  volcanic  vents)  considerably 
above  their  general  leveL  In  an  anticlinal  upheaval  they 
would  probably  conform  to  the  progress  of  the  sublevatory 
movement,  in  a  ratio  more  or  less  directly  proportional  to  the 
rapidity  of  the  upward  movement,  and  would  gradually  descend 
during  periods  of  repose.  This  would  happen  independently  of 
any  heat  generated  by  transformation  of  motion. 

In  a  polygenetic  chain  Uke  the  Sierra  Nevada,  after  the  coU 
lapse  and  folding  of  the  geosynclind  and  the  subsequent  stif- 
fening of  the  backbone  (so  to  speak),  any  further  elevation  of 
the  main  ridge  becomes  a  ^tioM-anticlinal  movement,  accom- 
panied necessarily  by  the  compression  and  "  squeesing "  of  the 
heated  rocks  embraced  within  the  arch.  The  heating  being 
greatest,  aeteris  paribus,  where  the  resistance  and  motion  is  a 
maximum,  more  heat  would  be  generated  by  the  compression 
of  the  upper,  half-stifiened  portion  of  the  viscous  or  igneoplastic 
layer,  than  in  the  lower  ones ;  and  the  liquid  matter  so  formed 
would  constitute  a  head  of  pressure,  from  which  fissure-erup- 
tions might  derive  their  material ;  whether  directly,  or  by  pres- 
sure communicated  to  more  distant  points  of  rupture  and  fusion 
by  lateral  stress. 

If,  then,  as  LeConte^s  data  seem  to  show,  the  final  and  most 
considerable  anticlinal  elevation  of  the  great  interior  range  took 
place  during  the  same  period  that  witnessed  the  great  fissure- 
eruptions  of  the  Coast  and  Cascade  ranges,  it  may  not  be  un- 
reasonable to  suppose  these  events  to  have  not  only  been  con- 
temporaneous, but  to  have  borne  to  each  other  something  of 
the  relation  of  cause  and  effect,  and  that  each  of  the  numerous 


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On  a  New  Formula  inDefinite  Integrals*  53 

saperimposed  strata  of  igaeoas  rock  in  the  latter  region  may 
represent  not  only  the  direct  effect  m  loco  of  more  or  less  par- 
oxysmal thrusts^  but  also  the  reflex  action  of  the  simultaneously 
progressing  anticlinals  in  the  high  Sierras. 


VII.  A  New  Formula  in  Definite  Integrals. 
By  J.  W.  L.  Glaishbr,  M.A*. 

1.  1  NT£6BATE  the  identity 

^-«i^+^----=i+^-^^(I^«  +  ^'^0(^  (1) 

(where  Aa«=:a»4.|~a»)  between  the  limits  zero  and  infinity^  and 
the  right-hand  side  becomes 

w 

=  1   (flocos*^— Aflotan«tfcos*tf+.,.)»«c*ft» 

w 

=  r'(flro- Atfo  Bin*  tf + A«flo  sin*  tf- . .  .)d0 
'tA      1  a  .  8    1  .o      5    8    1.-  \ 


so  that 


i 


The  definition  of  the  symbol  E  is  contained  in  Ea«=:a»4.i ;  and 
of  course,  a^  being  only  defined  for  n  a  positive  integer,  a.|  is 
without  meaning.  But  in  cases  where  On  involves  factorials,, 
there  is  a  strong  presumption,  derived  from  experience  in  similar 
questi9us,  that  the  formula  will  give  correct  results  if  the  conti- 
nuity of  the  terms  is  preserved  by  the  substitution  of  gamma 
functions  for  the  factorials.  This  I  have  found  to  be  true  in 
every  case  to  which  I  have  applied  (2). 

*  Commmiicated  by  the  Author. 


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64  Mr.  J.  W.  L.  Olaisher  an  a  New  Formula 

E.ff.{\)  Let 


1.2...(2n+l)"r(2n+2)  ' 
then  a-.^=l^  and 


i 


which  is  true, 
(u)  Let 

then 

and 

the  true  result. 


"'"  1.2...»  ~  r(n+l)' 

a-i         1 


^ '*  *^*  «•- n^n = rWTT)' '•  ^•^ 


X 


coBoadx^iO, 


TU.  sin  oossOj  the  value  we  should  expect  to  find  by  any  process 
that  gave  a  result  at  all. 

2.  Divide  (1)  by  1+^  and  integrate  as  before:  the  right- 
hand  side 

w 

=  j  (aoCOs«^-Afli>sin«^cos«^+A*aown*^cos«d— ...)iW 

TT/l      1    1  A  .  8    1    1  .o     5    8    1     1  ..^       \ 
=  2(2"4-2^+6-4-2^-5-r4-2^+---;^ 

•wv/ITA— 1^  _*»r        1 

2 A ''^"2l+-v/E^' 

so  that 

Take 

«*•  ^ 


1.2...2n      r(2n+l)' 


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in  Definite  Integrak.  55 

and 

J.  i+i«'^=2(i-''+r:2---r2''-  •  •  (*> 

Similarly,  by  taking  a»=s  ^       ,  we  obtain  the  correct  value  of 

®  X  sin  ax  , 
or. 


I 


The  peculiarity  of  (2)  and  (3)  consists  in  the  appearance  on 
the  right-hand  side  of  terms  with  fractional  arguments.  In  such 
an  equation  as  (4),  where  one  side  is  a  function  of  a^,  while  the 
other  involves  uneven  powers  of  a,  it  seems  as  though  it  would 
be  impossible  to  evaluate  the  integral  by  any  direct  procedure; 
for  d  priori  it  would  appear  that  no  method  of  expansion  and 
integration  term  by  term  could  transform  a  function  of  (f 
into  one  of  a,  and  thus,  as  it  were,  extract  the  square  root 
of  a  constant  involved.  The  way  in  which  the  symbolic  pro- 
cess introduces  i/£,  and  so  actually  does  effect  this  conver- 
sion, is  interesting:  when  I  first  applied  the  identity  (1)  to 
the  integral  in  (4),  I  scarcely  expected  to  obtain  any  result 
capable  of  interpretation. 

Whenever  (2)  and  (3)  admit  of  interpretation,  it  is  highly  pro- 
bable that  the  result  so  given  will  be  the  true  one ;  e.  g.,  taking 

1  +««'**- 2 lr(i)    r{|)  ^  r(2)    r(5)  +•  * •/ 

_ir  r        2a*    .  2at  ««  \ 

~2L       v^A       1.3      1.8-6  // 

the  known  vslae.  Bat  (2)  and  (3),  as  general  formule,  are  re- 
markable ;  and  diey  would  give  results  in  very  many  cases  where 
it  might  not  be  easy  to  evaluate  the  integrals  otherwise.        | 

Trinity  College,  Cambridge, 
June  19, 1874. 


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[    56    ] 

VIII.  On  some  Physical  Properties  of  Ice;  on  the  TVansposition 
of  Boulders  from  below  to  above  the  Ice ;  and  on  Mammoth" 
remains.    By  John  Rae,  M,D,,  LL.D.,  ifc*. 

IS  the  ice  formed  on  salt  water  fresh  f  or,  in  other  words,  if 
ice  formed  on  the  sea  is  thavred,  will  the  water  obtained 
thereby  be  fresh  ? 

For  a  number  of  years  past  I  have  spoken  with  many  persons 
on  the  above  subject;  and  seldom » if  ever,  have  I  found  a  single 
individual  who  did  not  say  that  the  ice  of  the  sea  was  fresh. 

Some  of  these  gentlemen  are  known  in  the  scientific  world ; 
and  many  of  them  supported  their  opinions  by  quoting  the 
highest  written  authorities  on  the  subject,  chiefly  Tyndall's 
'Forms  of  Water,'  p.  132,  par.  339,  which  tells  us  that  "even 
when  water  is  saturated  with  salt,  the  crystallizing  force  studi- 
ously rejects  the  salt,  and  devotes  itself  to  the  congelation  of 
the  water  alone.  Hence  the  ice  of  sea-water,  when  melted,  pro^ 
duces  fresh  water," 

It  IS  the  sentence  in  italics  to  which  I  wish  to  draw  particular 
attention. 

It  would  be  the  extreme  of  folly  and  presumption  on  my 
part  to  question  the  correctness  of  results  obtained  b^  scientific 
men  in  their  experiments  in  freezing  small  quantities  of  sea- 
water  by  artificial  means,  more  especially  those  of  the  distin* 
guished  gentleman  whose  name  I  have  mentioned,  who,  in 
addition  to  holding  the  high  position  of  being  one  of  our 
greatest  authorities  in  all  that  relates  to  physical  science,  pos- 
sesses the  rare  gift  of  being  able  to  communicate  his  knowledge 
in  such  plain,  clear,  and  forcible  language,  illustrated  by  admi- 
rable experiments,  as  to  make  his  meaning  fully  understood, 
even  by  those  who  had  previously  been  perfectly  ignorant  of 
the  subject. 

It  is  only  where  I  have  had  opportunities  of  witnessing  the 
action  of  cold  carried  on  in  a  manner  which  may  have  been 
denied  to  the  scientific  man,  that  I  venture  to  differ  from  him ; 
and  it  is  in  this  way  that  the  conviction  has  been  forced  upon 
me,  that  the  ice  of  sea-water  if  melted  does  not  produce  finesh 
water. 

Before  entering  upon  this  subject,  however,  let  me  say  a  word 
or  two  on  the  first  part  of  the  quotation  I  have  given. 

If  a  saturated  solution  of  salt  is  frozen,  and  the  ice  so  formed 
is  fresh,  it  is  evident  that  the  salt  that  has  been  ''rejected'^ 
must  be  deposited  or  precipitated  in  a  crystalline  or  some  other 
solid  form,  because  the  water,  if  any,  that  remains  unfrozen, 

*  Read  before  the  Physical  Society,  May  9, 1874.  Gommunicated  by 
the  Society. 


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Dr.  J.  Rae  an  same  Physical  Properties  qflce.         57 

h&ng  already  saturated^  can  hold  in  solution  no  more  salt  than 
it  already  contains. 

Could  not  salt  be  obtained  readily  and  cheaply  by  this  means 
from  sea- water  in  cold  climates  ? 

During  several  long  journeys  on  the  Arctic  coast^  in  the  early 
spring  before  any  thaw  had  taken  place^  the  only  water  to  be 
obtained  was  by  melting  snow  or  ice.  By  experience  I  found 
that  a  kettleful  of  water  could  be  obtained  by  thawing  ice  with 
a  much  less  expenditure  of  fuel^  and  in  a  shorter  time,  than 
was  required  to  obtain  a  similar  quantity  of  water  by  thawing 
snow.  Now,  as  we  had  to  carry  our  fuel  with  us,  this  saving  of 
fuel  and  of  time  was  an  important  consideration,  and  we  always 
endeavoured  to  get  ice  for  this  purpose.  We  had  another  in- 
ducement  to  test  the  sea-ice  frequently  as  to  its  freshness  or 
the  reverse. 

I  presume  that  almost  every  one  knows  that  to  eat  snow 
when  it  is  very  cold,  tends  to  increase  thirst,  whereas  a  piece  of 
ice  in  the  mouth  is  refreshing  and  beneficial,  however  cold  it 
may  be ;  we  were  consequently  always  glad  to  get  a  bit  of  fresh 
ice  whilst  at  the  laborious  work  of  hauling  our  heavy  sledges  ; 
yet  with  these  strong  inducements  we  were  never  able  to  find 
sea-ice,  in  situ*,  either  eatable  when  solid  or  drinkable  when 
thawed,  it  being  invariably  much  too  salt.  The  only  exception 
(if  it  may  be  cidled  one)  to  this  rule,  was  when  we  found  rough 
ice,  which,  from  its  wasted  appearance  and  irregular  form,  had 
evidently  been  the  formation  of  a  previous  winter.  This  old 
ice,  if  projecting  a  foot  or  two  above  the  water-level,  was  almost 
invariably  fresh,  and,  when  thawed,  gave  excellent  drinking- 
water.  It  may  be  said  that  these  pieces  of  fresh  ice  were  frag- 
ments of  glaciers  or  icebergs ;  but  this  could  not  be  so,  as  they 
were  found  where  neither  glaciers  nor  icebergs  are  ever  seen. 

How  is  this'to  be  accounted  for?  Unfortunately  I  have  only 
a  theory  to  o£fer  in  explanation. 

When  the  sea  freezes  by  the  abstraction  of  heat  from  its 
surface,  I  do  not  think  that  the  saline  matter,  although  retained 
in  and  incorporated  with  the  ice,  assumes  the  soUd  state,  unless 
the  cold  is  very  intense,  but  that  it  remains  fluid  in  the  form  of 
a  very  strong  brine  enclosed  in  very  minute  cells.  So  long  as 
the  ice  continues  to  float  at  the  same  level,  or  nearly  the  same 
level,  as  the  sea,  this  brine  remains ;  but  when  the  ice  is  raised 
a  little  above  the  water-level,  tbe  brine,  by  its  greater  specific 
gravity,  and  probably  by  some  solvent  quality  acting  on  the  ice, 
gradually  drains  off  from  the  ice  so  raised;  and  the  small  cells, 

*■  What  I  mean  by  ice  mi  situ  is  ice  lyin^  flat  and  unbroken  on  the 
sea,  as  formed  during  the  winter  it  is  formed  m. 


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58  Dr.  J.  Bae  on  the  IVaMpoiitum  ofBoulden 

by  eonnecting  one  with  another  downwards^  become  channek  of 
drainage. 

There  may  be  seTeral  other  requisiteB  for  this  change  of  salt 
ice  into  fresh^  sach  as  temperature  raised  to  the  freezing-point, 
so  as  to  enable  the  brine  to  work  out  the  cell-walls  into  channels 
or  tubes — that  is^  ifmy  theory  has  any  foundation  in  fact,  which 
may  be  easily  tested  by  any  expedition  passing  one  or  more 
winters  on  the  Arctic,  or  by  any  one  living  where  ice  of  con* 
siderable  thickness  is  formea  on  the  sea,  such  as  some  parts  of 
Norway. 

All  that  is  required,  as  soon  as  the  winter  has  advanced  £sr 
enough  for  the  purpose,  is  to  cut  out  a  block  of  sea-ice  (taking 
care  not  to  be  near  the  outflow  of  any  fresh-water  stream)  about 
8  feet  square,  remove  it  from  the  sea  to  some  convenient  posi- 
tion, test  its  saltness  at  the  time,  and  at  intervals  repeat  the 
testing  both  on  its  upper  and  lower  surfiEU^es,  and  observe  the 
drainage  if  any. 

The  result  of  the  above  experiment,  even  if  continued  for  a 
long  while,  may  not  be  satisfactory,  because  the  fresh  ice  that  I 
have  described  must  have  been  formed  at  least  twelve  months^ 
perhaps  eighteen  months,  before. 

The  JVanapoeition  of  Boulders  from  below  to  above  the  lee. 

When  boulders,  small  stones,  sand,  gravel,  8cc.  are  found 
lying  on  sea-ice,  it  is  very  generally  supposed  that  they  must 
have  rolled  down  a  steep  place  or  fallen  from  a  clifi*,  or  been 
deposited  by  a  flow  of  water  firom  a  river  or  other  source. 
There  is,  however,  another  way  in  which  boulders  &c.  get  upon 
floe-ice,  which  I  have  not  seen  mentioned  in  any  book  on  this 
subject. 

During  the  spring  of  1847,  at  Bepulse  Bay.  on  the  Arctic 
shores  of  America,  I  was  surprised  to  observe,  after  the  thaw 
commenced,  that  large  boulders  (some  of  them  3  or  4  feet  in 
diameter^  began  to  appear  on  the  surface  of  the  ice;  and  after  a 
while,  about  the  month  of  July,  th^  were  wholly  exposed, 
whilst  the  ice  below  them  was  sttong,  nrm,  and  something  like 
4  feet  thick. 

There  were  no  clifls  or  steep  banks  near  from  which  these 
boulders  could  have  come ;  and  the  only  way  in  which  I  could 
account  for  their  appearance,  was  that  which  by  subsequent 
observation  I  found  to  be  correct. 

On  the  shores  of  Bqpulse  Bay  the  rise  and  frdl  of  the  tide 
are  6  or  8  feet,  sometimes  more.  When  the  ice  is  forming  in 
early  winter,  it  rests,  when  the  tide  is  out,  on  any  boulders  &c. 
that  may  be  at  or  near  low-water  mark.    At  first,  whilst  the 


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fmm  behw  to  above  the  Ice.  59 

ice  18  weak,  the  boalden  break  through  it ;  but  whea  the  ice 
becomes  (say  2  or  3  fe^)  thick,  it  freezes  firmly  to  the  boulder, 
and  when  the  tide  rises,  is  strong  enough  to  lift  the  boulder 
with  it.  Thus,  once  fastened  to  the  ice,  the  stone  continues 
to  riae  and  fall  with  the  rise  and  fall  of  ^ush  tide,  until,  as  the 
winter  advances,  it  becomes  completely  enclosed  in  the  ice, 
which  by  measurement  I  found  to  attain  a  thickness  of  more 
than  8  feet 

SmaU  stones,  gravel,  sand,  and  shells  may  be  fixed  in  the 
iee  in  the  same  way. 

In  the  spring,  by  the  double  efiisct  of  thaw  and  evaporation, 
the  upper  surface  of  the  ice,  to  the  extent  of  S  feet  or  more,  is 
removeidy  and  thus  the  boulders,  which  in  autumn  were  lying 
at  the  bottom  <tf  the  sea,  are  now  on  the  ice,  while  it  is  stiU 
strong  and  thick  enough  to  travel  with  its  load,  before  favour- 
able winds  and  currents  to  a  great  distance. 

The  finding  small  stones  and  gravel  on  ice  out  to  sea  does  not 
always  prove  that  such  ice  has  been  near  the  shore  at  some  time 
at  other. 

I  have  noticed  that  wherever  the  Walrus  in  any  numbers 
have  been  for  some  time  lying  either  on  ice  or  rocks,  a  not 
inconsiderable  quantity  of  gravd  has  been  deposited,  apparently 
a  portion  of  the  excreta  of  that  animal,  having  probably  been 
taken  up  from  the  bottom  of  the  sea  and  swallowed  along  with 
their  food. 

Mammoth'remaiM.     The  position  in  which  their  Skeletons  are 
found,  Sfc, 

In  LyelFs  '  Principles  of  (Geology,*  vol.  i.  p.  186,  we  read  ^— 
''In  the  flat  country  near  the  mouth  of  the  Yenesei  river, 
Siberia,  between  latitudes  7(f  and  75*^  north,  many  skeletons  of 
mammoths,  retaining  the  hair  and  skin,  have  been  found.    The 
heads  of  most  of  these  are  said  to  have  been  turned  to  the  south/' 

As  fsur  as  I  -can  find,  the  distinguished  geologist  gives  no 
reason  why  the  heads  of  the  mammoths  were  turned  to  the 
south ;  nor  does  he  say  all  that  I  think  might  be  said  of  the 
reasons  why,  and  the  means  by  which  the  skins  have  been  pre- 
served for  such  a  long  period  of  time. 

Having  lived  some  years  on  the  banks  of  two  of  the  great 
rivers  of  America,  near  to  where  they  enter  Hudson's  Bay,  and 
also  on  the  M'Kenzie,  which  flows  into  the  Arctic  Sea,  1  have 
had  opportunities  of  observing  what  takes  place  on  these  streams^ 
all  of  which  have  large  alluvud  deposits,  forming  flats  and  shal« 
lows  at  iheir  mouths. 

What  I  know  to  be  of  common  occurrence  in  these  rivers 
may,  if  we  reason  by  analogy,  have  taken  place  in  ancient  timea 


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60  Dr;  J.  Rae  on  Mammoth-remains. 

on  the  great  rivers  of  Siberia,  making  due  allowance  for  the 
Dincb  higher  northern  latitude  to  which  these  streams  run  before 
reaching  the  sea,  and  for  the  difference  in  size  of  the  fauna  that 
used  to  frequent  their  banks. 

When  animals,  more  especially  those  having  horns,  tusks,  or 
otherwise  heavily  weighted  heads,  are  drifting  down  a  riv^, 
the  position  of  the  bodies  may  lie  in  any  dir^ion  as  regards 
the  course  of  the  stream,  as  long  as  they  are  in  water  deep 
enough  to  float  them ;  but  the  moment  they  get  into  a  shallow 
place,  the  head,  which  sinks  deepest  (or,  as  sailors  say,  ^^  draws 
most  water  *'),  takes  the  ground,  whilst  the  body,  still  remaining 
afloat,  swings  to  the  current,  just  as  a  boat  or  ship  does  when 
brought  to  anchor  in  a  tideway. 

It  is  probable  that  the  mammoths,  having  been  drowned  by 
breaking  through  the  ice  or  in  swimming  across  the  river  in 
spring  when  the  banks  were  lined  with  high  precipitous  drifts 
of  snow,  which  prevented  them  from  getting  out  of  the  water, 
or  killed  in  some  other  way,  floated  down  stream,  perhaps  for 
hundreds  of  miles,  until  they  reached  the  shallows  at  the  mouth, 
where  the  heads,  loaded  with  a  great  weight  of  bone  and  tusks, 
would  get  aground  in  8  or  4  feet  of  water,  whilst  the  bodies 
still  afloat  would  swing  round  with  the  current  as  ahready 
described. 

The  Yenesei  flows  from  south  to  north,  so  the  heads,  being 
pointed  up  stream,  would  be  to  the  south*. 

Supposing,  then,  these  bodies  anchored  as  above  in  8  or  4  feet 
water  ,*  as  soon  as  the  winter  set  in,  they  would  be  frosen  up  in 
this  position.  The  ice  in  so  high  a  latitude  as  70^  or  75^  north 
would  acquire  a  thickness  of  5  or  6  feet  at  least,  so  that  it  would 
freeze  to  the  bottom  on  the  shallows  where  the  mammoths  were 
anchored.  la  the  spring,  on  the  breaking  np  of  the  ice,  this 
ice  being  solidly  frozen  to  the  muddy  bottom,  would  not  rise  to 
the  surface,  but  remain  fixed,  with  its  contained  animal  remains, 
and  the  flooded  stream  would  rush  over  both,  leaving  a  covering 
of  mud  as  the  water  subsided. 

Part  of  this  fixed  ice,  but  not  the  whole,  might  be  thawed 
away  during  summer ;  and  (possibly,  but  not  nec^sarily)  next 
winter  a  fresh  layer  of  ice  with  a  fresh  supply  of  aninial  re- 
mains might  be  formed  over  the  former  stratum ;  and  so  the 
peculiar  position  and  perfect  state  of  preservation  of  this  ini« 

*  Not  many  yean  ago,  when  buiblo  were  very  abundant  on  the  Saskat* 
chewan,  hundreds  of  them  were  aometimea  drowned  in  one  seaaon  whilat 
awimming  acroaa  the  river;  and  many  reindeer,  mooae,  and  other  animala 
are  annually  destroyed  in  Uiia  way  in  other  large  American  rivers. 

Sir  Charlea  Lyell  mentiona  a  number  of  yaka  being  aeen  frozen  up  in 
one  of  the  Siberian  rivers,  which,  on  the  broking  up  of  the  ice  in  apnog, 
would  be  liberated  and  float  down  the  alream. 


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Mr.  F.  Clowes  on  a  Glass  Cell  with  Parallel  Sides.       61 

menae  collection  of  extinct  animals  may  be  accounted  for  without 
having  recourse  to  the  somewhat  improbable  theory  that  a  very 
great  and  sudden  change  had  taken  place  in  the  climate  of  that 
region. 

I  have  seen  at  the  mouth  of  Hayes  River  in  America  animals 
frozen  up  as  above  described ;  but  as  the  latitude  of  this  place  is 
only  57^  norths  the  fixed  ice  usually  wholly  di8apf>ear8  before 
the  next  winter  sets  in,  and  liberates  the  animals  shut  up  in  it ; 
but  when  the  rivers  reach  the  sea,  as  some  of  those  of  Siberia 
do,  1000  or  1200  miles  further  to  the  north,  it  may  be  fairly 
assumed  that  a  large  part  of  this  fixed  ice,  protected  as  i  would 
be  by  a  layer  of  mud,  might  continue  unthawed. 

IX.  Glass  Cell  with  Parallel  Sides. 
By  F.  Clowes,  Esq.,  B.Sc,  F.C.S.* 

THE  following  method  has  proved  very  convenient  for  making 
a  glass  cell,  which  may  be  readily  fitted  up  from  ordinary 
laboratory  apparatus,  and  may  also  be  rapidly  taken  to  pieces 
for  the  purpose  of  being  cleansed. 

A  piece  of  india-rubber  tubing  with  stout  walls,  or,  better,  a 
length  of  solid  rubber,  is  placed  pig.  | . 

in  the  form  of  a  letter  iJ  be- 
tween two  plates  of  glass,  the 
ends  of  these  plates  being  then 
firmly  held  together  by  slipping 
over  them  stout  in<ua-rubber 
rings.  A  glass  cell  is  thus  obtained,  the  parallel  faces  of  which 
are  formed  by  the  glass  plates,  whilst  its  thickness,  depth,  and 
length  can  be  suitably  varied  by  the  stoutness  and  length  of  the 
rubber  tube  and  the  shape  which  this  tube  is  made  to  assume. 

With  a  glass  cell  of  the  size  of  an  ordinary  magic-lantern 
slide  (fig.  1),  thedifierence  in  specific  gravity  between  hot  and 
cold  water  t  may  be  well  shown  upon  the  screen  by  a  magic 
lantern,  the  liquid  admitted  by  a  pipette  being  preferably  tinged 
by  dissolving  in  it  a  crystal  of  potassium  permanganate ;  and 
the  convective  currents  occurring  in  the  mass  of  a  liquid  may  be 
thrown  upon  the  screen  by  passing  a  galvanic  current  through 
a  fine  platinum  wire  stretched  between  two  thick  copper  wires 
beneath  the  surface  of  the  liquid  in  the  cell :  these  currents  are 
rendered  much  more  evident  by  allowing  the  platinum  wire  to 
be  immersed  in  a  stratum  of  potassium -permanganate  solution 
which  has  been  cautiously  introduced  beneath  the  water  by 
means  of  a  pipette  dipping  to  the  bottom  of  the  cell. 

*  Read  before  the  Physical  Society,  May  23,  1874.    Communicated  by 
tile  Socdetv* 
t  See  iVndairs  'Heat,  a  Mode  of  Motion,'  pp.  173  and  174. 


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flHF 

H 

^^1 

d3  Noticet  r$tj9eeHng  New  Books. 

A  smaller  cell  made  to  fit  into  the  wooden  firame  o(  a  kntern- 
riide  (fig.  2),  which  has  attached  Fig.  2. 

to  it  platinum  wires  connected 
by  copper  wires  and  binding- 
screws  with  a  galvanic  battery, 
serves  to  project  electrolytic  de- 
compositions npon  the  screen. 
Perhaps  the  most  beautifdl  ap- 
pearance is  that  presented  oy  th^  crystallucation  (^  the  metd 
from  a  solution  of  lead-acetate  which  is  undei^ing  electrolysis*. 

In  order  that  the  cell  mav  be  water-tight,  it  is  necessary  that 
the  india-rubber  rings  should  exert  a  somewhat  powerful  com- 

f)ression;  but  even  under  favourable  circumstances  slight 
eakage  is  liable  to  occur  in  about  half  an  hour  after  the  cell 
has  been  filled ;  this,  however,  would  allow  ample  time  for  the 
display  of  any  of  the  phenomena  above  alluded  to.  Rings  cut 
from  large-sized  india-rubber  tubing  have  been  found  wdl 
adapted  for  the  construction  of  small  cells. 


X.  Notices  respecting  New  Books. 

Text'Books  of  Science. — Principles  cf  Mechanics.  By  T.  M.  GkK)D- 
EYE,  M.A,j  Lecturer  on  Applied  Mechanics  at  the  Bcyal  School  of 
Mines,  London :  Longmans,  Green,  and  Co.  1874  (small  8vo, 
pp.  313). 
npHIS  book  contains  an  exposition  of  the  principles  of  mechanics, 
•^  such  as  is  commonly  given  in  elementary  treatises  on  that  sdenoe. 
The  exposition  is  illustrated  in  two  wa,ya— first  by  means  of  exam- 
ples of  the  ordinary  type,  secondly  by  reference  to  actual  mecha- 
nical contrivances  mainly  of  a  modem  character.  There  are  about 
a  hundred  and  eighty  illustrations  of  the  former  kind ;  and  of  these 
about  one  in  every  four  is  taken  from  the  Science  Examination 
papers  drawn  up  for  the  annual  examinations  of  the  Department 
of  Science  and  Art.  The  second  class  of  illustrations  constitutes 
the  chief  peculiarity  of  the  book,  and  unquestionably  its  most  valu- 
able part.  The  mere  names  of  some  of  these  illustrations  will  be 
enough  to  show  this — e.  g,  the  carrying  of  com  on  bands,  the  feed- 
ing of  running  trains  with  water,  the  disintegrating  flour-mill,  the 
ventilation  of  coal-mines,  the  lifting  of  coals,  the  stone-crushing 
machine,  Weston's  friction  coupling,  the  break-dnun,  the  crown 
valve,  the  blowing-engine,  the  hydraulic  accumulator,  the  hydnmlic 
crane,  &c.  These  form  an  assemblage  of  contrivances  which  have 
never  before,  to  our  knowledge  at  least,  been  described  in  any  ele- 
mentary book ;  they  render  the  work  before  us  worthy  of  the  study 
of  all  who  are  interested  in  mechanical  science ;  and  we  do  not 

•  Mr.  W.  Crookes,  F.R.S.,  Miggests  the  electrolysis  of  solution  of  thal- 
lium sulphate  as  furnishing  a  still  more  beautiful  example  of  crystallization. 


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Notices  reipecting  New  BocJm.  68 

Axibt  tbiit  these  iUnslrations  alone  will  csii«e  the  book  to  have,  as 
it  undoabtedlj  desenres  to  hare,  an  extensive  oircolatkm. 

It  wDl  be  evident  from  i^e  large  nnmber  of  contrivances  men- 
tioned in  ^e  above  list,  that  the  description  of  each  must  be  brief, 
and  that  the  attention  of  the  reader  is  mainlj  directed  to  the  dj- 
namical  principles  involved  in  their  use.  It  could  scarcely  fail  to 
happen,  undw  these  drcumstanoes,  tiiat  in  some  cases  p<nnts  in 
the  contrivances  are  not  quite  so  fully  described  as  the  reader 
might  wish.  In  others  the  contrivance  is  regarded  from  a  p<Hnt  of 
view  which  does  not  bring  quite  the  whc^  subject  under  notice ; 
and  tiiis  is  sometimes  a  little  misleading.  For  instance,  the  ooor 
trivanee  for  feeding  a  running  train  wi^  water  is  e<Misidered 
simply  as  an  illustration  of  inertia ;  and  this  probably  accounts  icft 
^ke  statement  that  the  water  which  runs  up  the  tube  *'  is  at  rest 
ezc^t  so  far  as  the  movement  in  a  vertical  direction  is  concerned  " 
(p.  49).  As  one  end  of  the  tube  is  vertically  over  the  other  end,  it 
is  plain  that  the  water  before  it  leaves  i^  tube  must  have  acquired 
Ihe  forward  velocity  of  the  train  as  well  as  ^  v^tacal  velocity 
with  which  it  ascends  the  tube ;  and  in  fact  the  illustration  of  thd 
inclined  plane^ushed  beneath  the  water  (p.  49),  if  properly  worked 
out,  shows  this  very  point :  e,  g,  conceive  a  particle  (P)  at  rest 
*  acted  on  by  no  forces,  and  an  inclined  plane  (with  an  angle  c) 
moving  forward  wit^  a  velocity  Y  to  come  into  contact  with  it ;  an 
instantaneous  action  takes  place  between  the  plane  and  the  point 
alcHig  the  perpendicular  to  the  plane ;  and  after  Ihe  action,  P  will 
move  with  a  uniform  velocity  aJong  a  line  in  space  coinciding  with 
the  position  of  the  perpendicular  at  the  instiuit  of  the  action.  If 
we  further  suppose  that  there  is  no  force  of  restitution,  P,  while 
moving  in  space  along  the  above-mentioned  line,  will  continue  to 
touch  the  plane  and  appear  to  run  up  it.  Supposing  the  mass  of 
the  plane  large  in  comparison  with  that  of  P,  the  horizontal  and 
vertical  components  of  Ps  velocity  will  be  V  sin' «  and  Y  sin  »  cos  «. 
It  is  evident  from  the  former  expression  that,  if  the  plane  were 
steep,  the  forward  horieontal  velocity  of  P  would  be  nearly  equal 
to  V,  and  would  be  quite  equal  to  it  if  the  plane  were  vertical. 
The  velocities  would  be  incr^tsed  if  there  were  restitution,  and  the 
point  would  be  thrown  forward  from  the  plane,  of  course  along  the 
aforesaid  perpendicular.  This  is  true  supposing  P  to  be  not  acted  on 
by  any  other  force  than  the  momentary  action  of  the  plane ;  if  we 
suppose  P  to  be  under  the  action  of  gravity,  the  above  vdodties 
are  its  horizontal  and  vertical  initial  velocities,  and  the  subsequent 
motion  can  be  easUy  determined  on  the  usual  suppositions.  Now 
the  contrivance  for  feeding  running  trains  with  water  differs  from 
the  case  we  have  been  considering  in  this — that  instead  of  a  mere 
inclined  plane,  a  tube  with  a  gradually  increasing  slope  is  em- 
ployed ;  the  effect  of  this  is  threefold :  in  th!^  first  places  the  increas- 
ing sl<^  makes  the  action  gradual  instead  of  instantaneous,  thereby 
diminishing  the  tendency  of  the  instrument  to  dash  the  water  out 
of  the  trough ;  in  the  neifft  place^  if  the  water,  when  once  in  the 
tube,  have  any  tendency  to  fly  forward  owing  to  restitution  or  any 


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64  Notices  respecting  New  Books. 

otiier  cause,  the  tendency  has  no  effect  so  far  as  the  presort  qaes«- 
tion  is  concerned ;  and,  finally,  as  the  tube  for  a  lai^  part  of  its 
.length  is  nearly  or  quite  rertical,  the  horizontal  velocity  of  the  as- 
cending stream  cannot  fail  to  acquire  the  forward  velocity  of  the 
train. 

The  Statement  of  General  Principles  and  the  proofs  of  particular 
theorems  contained  in  the  text  are  (it  is  almost  needless  to  say  so) 
correct  as  far  as  we  have  noticed ;  and  the  student  who  works  at 
the  book  conscientiously  will  doubtless  not  fail  to  make  it  out, 
though  the  style  does  not  generally  show  in  any  marked  degree  tiie 
power  of  clear  exposition.  There  is  one  point  which  ought  not  to 
be  left  unnoticed,  as  the  author  lays  considerable  stress  upon  it : 
he  states  that  he  has  endeavoured  '*  above  all  to  show  tiiat  the  re- 
lation of  the  theory  of  heat  to  mechanics  should  be  approached  by 
the  student  in  his  earliest  inquiries  with  the  same  careful  thought 
with  which  he  will  surely  regard  it  when  his  knowledge  and  his 
powers  have  become  extended  and  strengthened."  And  accordingly 
the  book  contains  articles  in  which  are  explained  what  is  meant  by 
the  mechanical  equivalent  of  heat,  by  the  kinetic  theory  of  gases, 
and  one  or  two  otner  matters.  What  parts  of  a  subject  an  author 
puts  into  his  book  is  a  matter  depending  so  much  on  his  own  judg- 
ment as  to  be  rarely  the  proper  subject  of  criticism ;  but  we  may 
perhaps  be  allowed  to  record  a  difference  of  opinion.  It  seems  to 
us,  then,  that  the  subject  of  energy  of  motion  presents  difficulties 
to  the  beginner  so  great  that  it  is  best  to  give  him  a  isxr  chance  of 
becoming  familiar  with  it  before  introducing  him  to  the  far  more 
difficult  subject  of  Potential  Energy,  and  accordingly  that  it  is  better 
not  to  deal  with  the  latter  subject  in  a  purely  elementary  treatise 
on  mechanics. 

EeUpses  Past  and  Future,  with  Oeneral  Hints  fcr  Observing  the  Heavens, 
By  the  £ev.  S.  J.  JomrsoH,  Parker  &  Co.:  Oxford  andLondcm. 
1874, 

Mr.  Johnson,  in  the  work  before  us,  has  added  considerably  to 
our  prospective  knowledge  of  eclipses,  transits,  and  allied  pheno- 
mena, and  has  also  given  us  some  interesting  information  relative 
to  ancient  eclipses,  mentioning  that  the  first  of  which  we  have  a 
clear  record  happened  at  Nineveh  in  the  year  763  b.c.  Noticing  in 
the  order  of  their  sequence  the  most  celebrated  eclipses  of  antiquity, 
and  bringing  up  the  catalogue  of  observed  eclipses  to  the  present 
date,  the  aumor  gives  us  two  interesting  chapters  (Y.  and  YI.) : — ^tiie 
first  on  the  prospects  of  the  amateur,  showing  the  paucity  of  large 
eclipses  in  England  during  the  next  thirty  years ;  and  the  second, 
"  Curiosities  in  Lunar  Echpses,"  as  bright  and  black  total  eclipses, 
and  those  in  which  both  luminaries  were  above  the  horizon  at  the 
time  of  the  moon  being  eclipsed,  an  obvious  effect  of  refraction. 
The  first  part  of  the  work,  m  which  we  have  notices  of  eclipses 
from  the  celebrated  one  of  Ho  and  Hi  2127  b.c.  October  13,  to 
A  j>.  2381  July  21,  contains  a  large  amount  of  information  on  an  in- 
teresting branch  of  astronomy. 


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Royal  Society^  G5 

From  edipsee  of  the  Sun  and  Moon,  the  author  passes  in  the 
second  part  of  his  work  to  describe  prospectirely  tiie  most  interes- 
ting planetary  phenomena,  the  periods  at  which  thej  may  be^  most 
adyantageoosly  looked  for,  with  the  peculiar  features  they  are  likely 
to  present.  Allusions  are  made  to  the  Aurora,  Zodiacal  light, 
Meteors,  &c. ;  and  we  notice  a  remarkable  suggestion  embodied  in  a 
communication  to  the  '  Spectator '  by  the  Bey.  E.  L.  Gkui)ett,  that 
the  cities  of  Sodom  and  Gk>morrah  were  destroyed  by  a  group  of 
tiie  meteors  following  TempeFs  telescopic  comet  of  1866.  Mr. 
Oarbett  giyes  six  reasons  for  his  suggestion  as  follows : — 

1.  From  the  deduced  period  of  node  passage  of  the  comet  a 
yifiit  must  haye  occurred  in  the  autumn  between  b.o.  1898  and  b.c. 
1897,  which  is  fl;enerally  assumed  as  the  date  of  the  catastrophe. 

2.  The  earth^  passage  of  node  was  on  July  31. 

3.  A  yertical  tiul  of  meteors  as  rain  was  only  possible  at  sunrise, 
the  hour  of  the  destruction  of  the  cities. 

4.  The  latitude  of  the  yertical  fall  agrees  with  that  of  the  cities. 

5.  Sodium,  the  chief  element  in  the  deposits  formed  in  the  loca- 
lity, is  the  chief  element  in  these  meteors  as  observed  by  Secchi. 

6.  Magnesium,  which  also  occurs  in  the  locality,  is  the  only  other 
ingredient  in  the  meteors  conspicuous  to  Secchi  by  means  of  the 
spectroscope. 

"  Suppose,"  says  the  writer,  "  any  eyent  not  due  to  this  comet  to 
be  recorded.  The  diances  against  the  account  presenting  these  six 
agreements  with  its  elements  and  no  disagreements,  are  three  mil* 
Hons  to  one  that  the  history  of  Sodom  is  true,  and  this  the  phy- 
sical cause.** 

The  work  closes  with  a  list  of  152  double  stars  and  nebul»,  ar- 
ranged  much  in  the  same  way  as  the  portion  on  the  Starry  Heayens 
of  Webb's  '  Celestial  Objects  for  Common  Telescopes,'  the  angles 
ci  position  of  the  double  stars,  as  seen  near  the  meridian,  being  in- 
dicated by  dots,  an  addition  which  we  haye  no  doubt  will  be  duly 
i^predated  by  those  readers  who  are  just  commencing  their  obser- 
vational career. 


XI.  Proceedings  qf  Learned  Soeieties. 

BOTAL  SOCIBTY. 
[Continued  from  toI.  zini.  p.  457.] 

December  11, 1873. — Joseph  Dalton  Hooker,  C.B.,  President, 
in  the  Chair. 

THE  following  communication  was  read : — 
"  On  the  Action  of  Heat  on  Grayitating  Masses."    By  Wil- 
liam Orookes,  FJEt.S.  &c. 

The  experiments  recorded  in  this  paper  haye  arisen  from  ob- 
senrations  made  when  using  the  yacuum-balance,  described  by  the 
author  in  his  paper  "On  ttie  Atomic  Weight  of  Thallium"*,  for 

»  PbiL  Tranf .  1873,  toL  olriii.  p.  277.  ,  " 

Phil.  Maj.  S.  4.  V(d.  48.  No.  815.  Jvly  1874,  F 


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66  Royal  Society  .—Mr.  W.  Crookes  on  the 

weigfainff  Bubetanoes  which  were  of  a  higher  temperature  than  the 
Burroanding  air  and  the  weights.  There  appeared  to  be  a  dimimi- 
tion  of  the  force  of  grayitation ;  and  experiments  were  instituted 
to  render  the  action  more  sensible,  and  to  eliminate  sources  of  error. 

In  an  historical  resume  of  the  state  of  our  knowledge  on  the  sub- 
ject oi  attraction  or  repulsion  by  heat,  it  is  shown  that  in  1702 
the  Bev.  A.  Bennet  recorded  the  fiict  that  a  light  substance  de- 
licately suspended  in  air  was  attracted  by  warm  bodies :  this  he 
ascribed  to  air-currents.  When  light  was  focused,  by  means  of  a 
lens,  on  one  end  of  a  delicately  suspended  arm,  eitiier  in  air  (Mr  in 
an  exhausted  receiver,  no  motion  could  be  perceiyed  distinguish- 
able from  the  efEects  of  heat. 

Laplace  spoke  of  the  repulsive  force  of  heat.  Libri  attributed 
the  movement  of  a  drop  of  liquid  along  a  wire  heated  at  one  end, 
to  the  repulsive  force  of  heat ;  but  Baden  Powell  did  not  succeed 
in  obtaining  evidence  of  repulsion  by  heat  from  this  experiment. 

Fresnel  described  an  experiment  by  which  concentrated  solar 
light  and  heat  caused  repulsion  between  one  delicately  suspended 
and  one  fixed  disk.  The  experiment  was  tried  in  air  of  different 
densities ;  but  contradictory  results  were  obtained  under  apparently 
similar  circumstances  at  different  times,  and  the  experiments  weto 
not  proceeded  with. 

Saigey  described  experiments  which  appeared  to  prove  that  a 
mark^  attraction  existed  between  bodies  of  different  temperaturea. 

Forbes,  in  a  discussion  and  repetition  of  Trevelyan  s  experi- 
ment, came  to  the  conclusion  that  there  was  a  repulsive  action  ex<- 
erdsed  in  the  transmission  of  heat  from  one  body  into  another 
which  had  a  less  power  of  conducting  it. 

Baden  Powell,  r^eating  Fresners  experiment,  explained  l^a 
results  otherwise  than  as  due  to  repulsion  by  heat.  By  observing 
the  descent  of  the  tints  of  Newton's  Bings  between  glass  pliU«s  when 
heat  was  applied,  Baden  Powell  showed  that  the  interval  between 
theplatea  increased,  and  attributed  this  to  a  repulsive  action  of  heat^ 

Faye  introduced  the  hypothesis  of  a  repulsive  force  of  heat  to 
account  for  certain  astronomical  phenomena.  He  described  an 
experiment  to  show  that  heat  produced  repulsion  in  the  luminoua 
arcjriven by  an  induction-coil  ii^  rarefied  air« 

l£e  author  describes  numerous  forms  of  apparatus  successivelj 
more  and  more  delicate,  which  enabled  him  to  detect  and  then  to 
render  very  sensible  an  action  exerted  by  heat  on  gravitating  bodies, 
which  is  not  due  to  air-currents  or  to  any  other  known  form  of 
fwce. 

The  following  experiment  with  a  balance  made  of  a  straw  beam 
with  pith-ball  masses  at  the  ends  enclosed  in  a  glass  tube  and  con- 
nectea  with  a  Sprengel  pump,  may  be  quoted  from  the  paper : — 

<*  The  whole  being  fitted  up  as  here  shown,  and  the  i^paratus 
being  full  of  air  to  begin  with,  I  passed  a  spirit-fiame  across  the 
lower  part  of  the  tube  at  6,  observing  the  movement  by  a  low-power 
micrometer;  the  pith  ball  (a,  h)  descended  slightly,  and  then  im- 
mediately rose  to  considerably  above  its  originaJ  position.     It 


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Action  of  Heat  on  Gravitating  Masses,  67 

seemed  as  if  the  trae  action  of  the  heat  was  one  of  attraction,  in- 
Btantiy  oyercome  bj  ascending  currents  of  air 

"  31.  In  order  to  apply  the  heat  in  a  more  reguUr  manner,  a 
tii^mometer  was  inserted  in  a  glass  tube,  having  at  its  extremity 
a  glass  bulb  about  1|  inch  in  diameter ;  it  was  filled  with  water  and 
then  sealed  up. .  .  The  water  was  kept  heated  to  ,70^  C,  the  tem- 
peratnre  of  the  laboratory  being  about  15°  0. 

^*  32.  The  barometer  being  at  767  milUms.  and  the  gauge  at  zero, 
tiie  hot  bulb  was  placed  beneath  the  pith  ball  at  h.  The  ball  rose 
n^dly ;  as  soon  as  equilibrium  was  restored,  I  placed  the  hot- 
water  bulb  above  the  pith  ball  at  a,  when  it  rose  again,  more  slowly, 
however,  than  when  the  heat  was  applied  beneath  it. 

•*  33.  The  pump  was  set  to  work ;  and  when  the  gauge  was  147 
miUims.  below  the  barometer,  the  experiment  was  tried  again ;  the 
same  result,  only  more  feeble,  was  obtained.  The  exhaustion  was 
continued,  stopping  the  pump  from  time  to  time,  to  observe  the 
effect  of  heat,  when  it  was  seen  that  the  effect  of  the  hot  body 
regularly  diminished  as  the  rarefaction  increased,  until  when  the 
gauge  was  about  12  miUims.  below  the  barometer  the  action  of 
the  hot  body  was  scarcely  noticeable.  At  10  millims.  below  it  was 
still  less  ;  whilst  when  there  was  only  a  difference  of  7  millims.  be- 
tween the  barometer  and  the  gauge,  neither  the  hot-water  bulb, 
the  hot  rod,  nor  the  spirit-flame  caused  the  ball  to  move  in  an  ap- 
preciable degree.  The  inference  was  almost  irresistible  that  the 
rising  of  the  pith  was  only  due  to  currents  of  air,  and  i^at  at  this 
near  approach  to  a  vacuum  the  residual  air  was  too  highly  rarefied 
to  have  power  in  its  rising  to  overcome  the  inertia  c^  the  straw 
beam  ana  the  pith  balls.  A  more  delicate  instrument  would  doubt- 
less show  traces  of  movement  at  a  still  nearer  approach  to  a  vacuum ; 
but  it  seemed  evident  that  when  the  last  trace  of  air  had  been  re- 
moved from  the  tube  surrounding  the  balance — when  the  balance 
WES  suspended  in  empty  space  only — the  pith  ball  would  remain 
motionless,  wherever  the  hot  body  vrere  applied  to  it. 

^  34.  I  continued  exhausting.  On  next  applying  heat,  the  result 
showed  that  I  veas  hr  from  having  discoveied  the  law  governing 
tiliese  phenomena;  the  pith  ball  rose  steadily,  and  without  that 
hesitation  which  had  been  observed  at  lower  rarefactions.  With  the 
gaoge  3  millims.  below  the  barometer,  the  ascension  of  the  pith 
when  a  hot  body  was  placed  beneath  it  was  equal  to  what  it 
had  been  in  air  of  ordinary  density ;  whilst  with  the  gauge  and 
barometer  level  its  upward  movements  were  not  only  sharper  than 
they  had  been  in  air,  but  they  took  place  under  the  influence  ci 
£nr  less  heat ;  tbe  fii^^er,  for  example,  instantly  sending  the  ball  up 
to  its  fullest  extent.** 

A  piece  of  ice  produced  exactlythe  opposite  effect  to  ahotbody. 

Numerous  experiments  are  next  given  to  prone  that  the  action 
is  not  dae  to  efeetridty. 

The  presence  of  air  having  so  marked  an  influence  on  the  action 
ol  heat,  an  apparatus  was  fitted  up  in  whidi  the  source  of  heat  (a 
platinum  spiral  rendered  incandescent  by  electricity)  was  inside  the 

F2 


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68  Royal  SocUty  .—Mr.  W.  Crooket  on  the 

Yftouum-tube  inatead  of  outoide  it  as  bef(»e ;  and  the  pith  balls  ol 
the  former  apparatus  were  replaced  by  brass  balls.  By  careful  mar 
nagement  and  turning  the  tube  round,  the  author  could  place  the 
equipoised  brass  pole  either  over,  under,  or  at  the  side  of  the  source 
of  heat.  With  this  apparatus  it  was  intended  to  ascertain  mcHre 
about  the  behaviour  of  the  balance  during  the  progress  of  the  ex- 
haustion, both  below  and  above  the  point  of  no  action,  and  also  to 
ascertain  the  pressure  corresponding  with  this  critical  point. 

After  describing  many  experiments  with  the  ball  in  various  po- 
sitions with  respect  to  the  incandescent  spiral,  and  at  different 
pressures,  the  general  result  is  expressed  by  the  statement  that 
the  tendency  in  each  case  was  to  bring  the  centre  of  gravity  of  the 
brass  ball  as  near  as  possible  to  the  sourbe  of  h^^t,  when  air  of  or- 
dinary density,  or  even  highly  rarefied  air,  surrounded  the  balance. 
The  author  continues  : — 

*'  44.  The  pump  was  then  worked  until  the  gauge  had  risen  to 
within  5  millims.  of  the  barometric  height.  On  arranging  the  ball 
above  the  spiral  (and  making  contact  with  the  battery),  the  attrac- 
tion was  still  8tr<»ig.  drawing  the  baU  downwards  a  distance  of  2 
millims.  The  pump  continuing  to  work,  the  gauge  rosauntil  it  was 
within  1  milHm.  of  the  barometer.  The  attraction  of  the  hot  spiral 
for  the  ball  was  still  evident,  drawing  it  down  when  placed  below 
it,  and  up  when  placed  above  it.  The  movement,  however,  was 
much  less  decided  than  before ;  and  in  spite  of  previous  experience 
(33,  34)  the  inference  was  very  strong  that  i£e  attraction  would 
gradually  diminish  until  the  vacuum  was  absolute,  and  that  then, 
and  not  till  then,  the  neutral  point  would  be  reached.  Within  one 
millimetre  of  a  vacuum  there  appeared  to  be  no  room  for  a  change 
of  sign. 

*'  45.  The  gauge  rose  until  there  was  only  half  a  millimetre  be- 
tween it  and  the  barometer.  The  metallic  hammering  heard  when 
the  rare&ctioQ  is  dose  upon  a  vacuum  commenced,  and  the  fillip- 
ing mercury  only  occasionally  took  down  a  bubble  of  air.  Oa 
turning  on  the  battery  current,  there  was  the  faintest  possible 
movement  of  the  brass  ball  (towards  the  spiral)  in  the  direction  ol 
attraction. 

.  "  46.  The  working  of  the  pump  was  continued.  On  next  ma- 
king contact  with  the  battery,  no  movement  could  be  detected. 
The  red-4ot  spinJ  nmther  attracted  nor  repelled  I  had  arrived  at 
the  critical  point.  On  looking  at  the  gauge  I  saw  it  was  level  with 
the  barometer. 

**  47.  The  pump  was  now  kept  at  full  work  for  an  hour.  The 
gauge  did  not  rise  perceptibly ;  but  the  metiJlic  hammering  sound 
increased  in  sharpness,  and  I  could  see  that  a  bubble  or  two  ol  air  had 
been  carried  down.  On  igniting  the  spiral,  I  saw  that  the  critical 
point  had  been  passed.  The  sign  had  changed,  and  the  action  was 
mnt  but  unmistakable  repuUum.  The  pump  was  still  kept  going, 
and  an  observation  was  taken  from  time  to  time  during  several 
hours.    The  repulsion  continued  to  increase.     The  tubes  of  the 


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Action  of  Htat  ok  QravUating  Ma$i€$.  69 

pump  were  now  washed  oat  witii  oil  of  Titriol*,  and  the  working 
was  ocmtinued  for  an  hoar. 

'^  48.  The  aeti(m  of  the  incandescent  sniral  was  now  |oand  to  ba 
exiesr^UcaIljrq>dlefU,  whether  it  was  placed  aboTe  or  below  the 
brass  ball.  The  finsers  exerted  a  repeUent  action,  as  did  also  a  warm 
glass  rod,  a  spirit-lame,  and  a  niece  of  hot  oopper.** 

In  order  to  decide  once  for  all  whetiier  these  actions  really  were 
dueto-aar-carrents,  a  form  of  apparatas  was  fitted  op  which,  whilst 
it  woold  settle  the  qoestion  indispatablj,  woald  at  the  same  time 
be  likel J  to  afford  information  <^  mach  interest. 

Bj  chemical  means  the  author  obtained  in  an  apparatus  a  Tacuam 
so  neariy  perfect  that  it  would  not  carry  a  current  inm  ^  Buhm-^ 
ko^s  coil  when  connected  with  platinum  wires  sealed  into  the 
tube.  In  such  a  vacuum  the  repulsion  by  heat  was  still  found  to 
be  decided  and  energetic. 

An  experiment  is  next  described,  in  whidi  the  rays  of  the  sun, 
and  then  ihe  di&rent  portions  of  the  solar  spedrum,  are  projected 
on  to  the  delicately  suspended  pit^ball  balance.  In  vacuo  the 
repulsion  is  so  strong  as  to  cause  danger  to  the  apparatus,  and 
resembles  that  which  would  be  produced  by  the  physical  impact  of  a 
material  body. 

Experiments  are  next  described  in  which  various  substances  were 
used  as  the  gravitating  masses.  Amongst  these  are  ivory,  brass, 
pith,  platinum,  gilt  pith,  silver,  bismuth,  selenium,  copper,  mica 
(horisontal  and  vertioJ),  charcoal,  Ac. 

The  behaviour  of  a  glass  beam  with  glass  ends  in  a  diemical  va- 
cuum, and  at  lower  exhaustion,  is  next  accurately  examined  when 
heat  is  applied  in  different  ways. 

On  suspending  the  light  index  by  means  of  a  cocoon  fibre  in  a 
kmg  glass  tube  furnished  with  a  bulb  at  the  end,  and  exhausting 
in  various  ways,  the  author  finds  that  the  attraction  to  a  hot  bodv 
in  air,  and  the  repulsion  from  a  hot  body  in  vacuo  are  rendered  stiu 
more  apparent. 

Speaking  of  Cavendish's  celebrated  experiment,  the  author  says 
^bat  he  has  experimented  for  some  months  on  an  apparatus  of  this 
kind,  and  gives  the  following  outline  of  one  of  the  results  he  has 
obtained : — 

<'  A  heavy  metaUic  mass,  when  brought  near  a  delicately  sus- 
pended light  ball,  attracts  or  repels  it  under  the  following  circum- 
stances:— 

''  I,   WJten  ike  ball  ia  in  air  of  ordinary  density. 

a.  If  the  mass  is  colder  than  the  ball,  it  repels  the  ball. 
6.  If  the  mass  is  hotter  than  the  ball,  it  aUraets  the  ball. 
**  II.   When  the  baU  is  in  a  vacuum. 

a.  If  the  mass  is  colder  than  the  ball,  it  attracts  the  ball. 
h.  If  the  mass  is  hotter  than  the  ball,  it  repels  the  ball." 

The  author  continues: — *'  The  density  of  the  medium  surround- 

*  This  can  be  effected  without  interfering  with  the  eihmusiion. 


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70  Royal  Sbdeiy : — 

ii^  tii0  bttB,  the  mfttonal  of  \diich  the  ball  is  nuMle,  and  a  Tsty 
«l]£ht  difference  between  the  temperatures  of  the  mass  and  tbi 
baU,  exert  so  strong  an  ii^umiee  over  the  attraotiTe  and  ropulsiYe 
force,  and  it  has  be^  so  difficult  for  Bie  to  eliminate  all  interfeiiDg 
actioDs  of  temperature,  eleotrioity,  Ac,  that  I  have  not  yet  been 
aUe  to  get  distinct  evidence  of  an  independent  force  (not  being  of 
the  nature  of  heat)  urging  the  ball  and  the  mass  tqgeUiw. 

«*  Experiment  has,  however,  showed  me  that,  whilst  the  action  is 
in  one  dhrection  in  dense  air,  and  in  the  <^posite  direction  in  a 
vacuum,  there  is  an  intermediate  pressure  at  whidi  differences  of 
tampeiwture  appear  to  exert  little  or  no  interfering  action.  By 
experimenting  at  this  critical  pressure,  it  would  seem  that  such  an 
action  as  Was  obtained  by  Cavendish,  Beidi,  and  Baily  should  be 
rendered  evideaxt.'' 

After  discussing  the  explanations  which  may  be  given  iA  these 
actions,  and  i^owing  that  they  cannot  be  due  to  auMnirrents,  the 
author  refers  to  evidences  of  this  repulsive  action  of  heat,  and  at- 
kactive  action  of  cold,  in  nature.  In  that  portion  of  Uie  sun's 
radiation  which  is  called  heat,  we  have  the  radial  repulsive  f  oroe^ 
possessing  successive  propagation,  required  to  explain  the  phenc^- 
mena  of  comets  and  the  shape  and  changes  of  the  nebnl».  To 
compare  small  things  with  great-— to  argue  from  pieces  of  straw  up 
to  heav^ily  bodies— it  is  not  improbable  that  the  attraction,  now 
shown  to  exist  between  a  cold  ana  a  warm  body,  vdll  equally  prevail 
when,  for  the  temperature  of  meltine  ice  is  substituted  the  cold  of 
space,  f <»r  a  pith  oall  a  celestial  sphere,  and  for  an  artificial  van 
cuum  a  stellar  vmd.  In  the  radiant  molecular  energy  ci.  cosmical 
masses  may  at  last  be  found  that  "  agent  acting  constantlv  accord- 
ing to  certain  laws,"  which  Newt<m  held  to  be  the  cause  of  gravity. 

January  8, 1874, — Joseph  Dalton  Hooker,  G.B.,  President,  in 
the  Qiair. 

The  following  communication  was  read : — 

"  On  Electrotorsion.**    By  G^eo^ge  Gore,  P.E.S. 

This  communication  contains  an  account  of  a  new  phenomenon 
(of  rods  and  wires  of  iron  becoming  twisted  while  under  the  in- 
fluence of  electric  currents),  and  a  full  description  of  the  con- 
ditions under  which  it  occurs,  the  necessary  apparatus,  and  the 
methods  of  using  it. 

The  phenomenon  of  torsion  thus  produced  is  not  a  microscopic 
one,  but  may  be  made  to  exceed  in  some  cases  a  twist  of  a  quarter 
of  a  circle,  the  end  of  a  suitable  index  moving  through  a  space  of 
80  centimetres  (be31  inches).  It  is  always  attended  by  emission 
of  sound. 

The  torsipns  are  produced  by  the  combinea  influence  of  helical 
and  axial  dectric  currents,  one  current  passing  through  a  long 
copper-wire  cml  surrounding  the  bar  or  wire,  and  the  other,  in 
an  axial  direction,  through  the  iron  itself.  The  cause  of  them  is  the 
combined  influence  of  magnetism  in  the  oidinary  longitudinal  direc- 


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Mr.  6.  Gore  on  Bk^rot€Tium.  91 

tion  inAaoed  in:  liie  bar  by  the  ooil-cnrrent,  and  transterse  mag- 
netism  indueed  in  it  by  the  axial  one. 

The  torsions  are  remsibbl j  symmetrical,  and  are  as  definitely 
lebted  in  dbreclaon  to  dectric  currents  as  magnetism  itself.  The 
chief  law  of  them  is — A  current  Jhwing  from  a  norih  to  a  90%Uh 
pole  produces  left-handed  toreion,  cmd  a  reveree  one  rtg7u4uxnded  tor^ 
non  (L  e.  in  the  direction  of  an  ordinary  screw).  Although  eadbi 
eorrmt  ahme  will  produce  its  own  magnetic  effect,  sound,  and  in- 
ternal molecular  morement,  neither  al<me  will  twist  the  bar,  unless 
the  bar  has  been  preyiously  maenetised  by  the  other.  Suceessiye 
coil-eurrents  alone  in  opposite  oirections  will  not  produce  torsion, 
neither  will  suceessiye  and  opposite  axial  ones. 

Hie  torsions  are  influenced  by  previous  mechanical  twist  in  the 
iron,  by  mechanical  tension,  and  by  terrestrial  magnetic  induction. 
The  direction  of  them  depends  both  upon  that  of  the  axial  and  of  the 
oofl-currents,  but  appears  to  be  determined  most  by  the  former.  A 
few  cases  occur  in  which  the  currents,  instead  of  developing  torsion, 
produce  detorsion ;  but  only  two  instances,  out  of  many  hundreds, 
have  been  met  with  in  which  torsion  was  produced  in  a  direction 
opposite  to  that  required  by  the  law. 

Bingle  torsions  vary  in  magnitude  from  0*5  mUlim.  to  nearly  30 
millims.  of  movement  of  the  end  of  an  index  47  centimetres  long ; 
the  smaller  ones  occur  when  the  two  currents  are  transmitted 
alternately,  and  the  large  ones  when  they  are  passed  simultane- 
ously ;  the  former  generally  leave  the  bar  in  a  twisted  state,  the 
latter  do  not.  Those  produced  by  axial  currents  succeeding  coil 
ones  are  nearly  always  much  larger  than  those  yielded  by  ooU-cur- 
rents  succeeding  axiiu  ones,  because  the  residual  magnetism  left  by 
ttie  coil-current  is  the  strongest.  The  order  of  succession  of  ihe 
currents  affects  the  torsions  in  all  cases,  altering  their  magnitudes, 
and  in  some  few  instances  even  their  directions.  In  steel  all  the 
torsional  effects  are  modified  by  the  mechanical  and  magnetic 
properties  of  that  substance. 

Each  current  leaves  a  residuary  magnetic  effect  in  the  bar, 
amounting  in  iron  to  about  one  tenth  of  its  original  influence.  The 
residuary  magnetism  of  coil-currents  is  affected  and  sometimes  re- 
versed by  axial  ones ;  and  that  of  axial  currents  is  also  removed  by 
coil  ones,  and  by  a  red  heat.  The  condition  left  by  an  axial  current 
is  smaller  in  degree  and  less  stable,  in  a  vertical  iron  wire  or  one  in 
the  terrestrial  magnetic  meridian,  than  that  left  by  a  coil  one,  partly 
because  of  the  influence  of  terrestrial  magnetism ;  but  in  a  position 
at  right  angles  to  that  the  effect  is  different. 

The  torsion  produced  by  a  coil-current  may  be  used  as  a  test, 
imd  partly  as  a  measure,  of  the  residuary  effect  of  an  axial  one ; 
and  that  produced  by  an  axial  currrait  may  be  employed  to  detect, 
and  to  some  extent  measure,  ordinary  magnetism  in  the  bar.  As 
an  opposite  coil-current  at  once  reverses  the  ordinary  longitudinal 
magnetism  of  a  bar  of  iron,  so  also  an  opposite  axial  one  at  once 
reverses  its  transverse  magnetism. 

Many  instances  have  been  met  with  in  which  the  transverse  and 


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78  Oeoloffical  Society : — 

kmfltudiBal  magnetic  stateB  produced  bj  the  two  currraits  coen- 
istea  in  the  same  substance.  The  tinrsional  influence  of  the  ex- 
cited heHz  is  distributed  equally  throughout  its  l^agth ;  so  also  is 
that  of  the  current  in  the  bar.  AU  the  torsions  are  doselj  reUted 
to  the  well-known  electric  sounds,  and  to  particular  positions  and 
internal  moyements  of  the  particles  of  the  iron. 

Signs  of  electrotorsion  were  obtained  with  a  bar  of  nickel,  bat 
not  with  wires  of  pUitinum,  silver,  copper,  lead,  tin,  cadmium, 
sine,  magnesium,  aluminium,  brass,  or  German-silTer,  nor  with 
a  tldak  rod  of  sine,  or  a  cord  of  gutta  percha. 


eEOLOOICAL  80CIBTY. 

[Continiied  from  toI.  zlvii.  p.  462.] 

June  25,  1873.— Joseph  Frestwich,  Esq.,  F.B.S.,  Yice-Preeident, 

in  the  Chair. 
'  The  following  communications  were  read : — 

1.  '*  On  six  Lake-basins  in  Argyllshire."  By  His  Grace  the  Duke 
of  Argyll,  K.T.,  F.R.S.,  President 

The  author  referred  to  the  part  ascribed  to  glacial  action  in  the 
formation  of  lake-basins,  and  described  the  basins  of  six  lakes  in  Ar- 
gyllshire, the  characters  presented  by  which  seemed  to  him  incon- 
sistent with  their  having  been  excayated  by  ice.  Among  these  lakes 
were  Loch  Fyne,  Loch  Awe,  Loch  Leokan,  and  the  Dhu  Loch.  The 
upper  part  of  Loch  Fyne  was  said  to  be  out  off  fh>m  the  rest  by  a  bar 
of  islands,  with  only  one  or  two  deeper  passages.  The  country  about 
Loch  Fyne  was  described  as  consistiog  of  Upper  and  Lower  l^urian 
mica-slates,  which  have  been  violently  contorted,  their  normal  strike 
being  indicated  by  the  direction  of  the  valleys.  Loch  Fyne  occupies 
a  niche  in  the  slope  of  the  rocks,  having  an  escarpment  on  one  side 
and  the  shelving  strata  on  the  other,  ^e  existence  of  a  fault  along 
the  line  of  the  loch  was  probable,  but  could  not  easily  be  ascertained. 
Its  greatest  depth  in  this  part  was  said  to  be  84  fathoms.  Its 
banks  show  marks  of  glaciation,  whereon  the  sur&oe  is  well  adapted 
for  their  preservation ;  the  strongest  marks  are  on  those  rock-faces 
which  look  up  the  loch.  Between  Loch  Fyne  and  Loch  Awe  the 
mica-slates  are  interstratified  with  granite,  which  the  author  be- 
lieved to  have  been  forced  up  between  the  plains  of  stratification  by 
the  pressure  caused  by  the  falling  in  of  the  mica-slates,  as  frag- 
ments of  the  latter  rock  are  imbedded  in  the  granite.  The  author 
described  the  different  structure  of  the  two  banks  of  Loch  Awe,  the 
upper  part  of  which  seemed  to  him  to  lie  in  a  synclinal  trough ;  and 
its  waters  were  only  prevented  by  a  low  col  from  finding  their  way 
to  the  Atlantic  in  this  direction,  instead  of  from  the  lower  end. 
The  formation  of  the  basin  of  Loch  Awe  seemed  to  the  author  to  be 
due  solely  to  geological  structure,  as  vras  also  the  case  with  another 
lake  beyond  the  head  of  Loch  Awe.  The  surrounding  country  was 
said  to  be  full  of  smaller  lake-basins,  the  formation  of  which  might 
be  due  to  the  denudation  of  the  softer  mica- schists  lying  below  the 


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Prof.  R.  Owtn  on  the  SkuU  of  a  dentigerous  Bird.        78 

gnmite  ridges.  But  in  some  cases  the  basins  were  excavated  in  the 
latter;  Loch  Leckan  was  mentioned  as  an  example.  It  is  about  a  mile 
long,  from  100  to  200  yards  broad,  and  no  less  than  18  Ifiathoms  deep. 
At  the  top  of  its  southern  bank,  which  consists  of  granite,  there  is 
another  lake  (Loch-nar-Craig),  about  200  yards  broad  and  9  fathoms 
deep.  The  surrounding  hUls  are  low,  and  there  appeared  to  be  no 
source  which  could  furnish  ice  to'excavate  a  lake  of  such  depth  as  Loch 
Leckan ;  and  further,  the  author  contended  that  if  one  of  these  two 
basins  had  been  excavated  by  ice,  the  other  could  hardly  have  been 
preserved  intact.  Two  other  lakes,  excavated  on  the  summits  of 
granite  ridges,  were  mentioned;  and  the  author  could  not  conceive 
how  either  a  glacier  or  an  ice-cap  could  have  produced  such  basins. 
The  Dhu  Loch,  separated  from  Loch  Fyne  by  a  bank  of  gravel  about 
a  mile  broad,  is  entirely  in  detrital  matter,  which  the  auUior  thought 
might  have  been  accumulated  in  its  present  form  by  the  sea  beating 
against  the  end  of  a  glacier.  From  its  position  and  level,  the  Dhu 
Loch  rises  and  falls  with  the  tide;  and  it  would  appear  that  it 
formerly  extended  some  miles  furUier  up  the  valley,  where  the 
author  had  found  days  containing  a  mixture  of  marine  and  fresh- 
water DiatomacesB.  In  five  of  these  cases  the  author  thought  it  was 
impossible  that  the  basins  are  due  to  glacial  action. 

2.  <'  Description  of  the  Skull  of  a  dentigerous  Bird  {Odantopteryx 
uHiapiais,  Owen),  from  the  London  Clay  of  Sheppey."  By  Prof. 
Kichard  Owen,  F.R.S.,  F.G.S. 

The  specimen  described  by  the  author  consisted  of  the  brain-case, 
with  the  basal  portion  of  both  jaws.  The  author  described  in  detail 
the  structure  and  relations  of  tiie  various  bones  composing  this  skull, 
which  is  rendered  especially  remarkable  by  the  denticulation  of  the 
alveolar  margins  of  the  jaws,  to  which  its  generic  appellation  refers. 
The  denticulations,  which  are  intrinsic  parts  of  the  bone  bearing 
them,  are  of  two  sizes, — ^the  smaller  ones  about  half  a  line  in  length, 
the  larger  ones  from  two  to  three  lines.  The  latter  are  separated 
by  intervals  of  about  half  an  inch,  each  of  which  is  occupied  by 
several  of  the  smaller  denticles.  All  the  denticles  are  of  a  triangular 
or  compressed  conical  form,  the  larger  ones  resembling  lania- 
riee.  Sections  of  the  denticles  show  under  the  microscope  the  un- 
mistakable characters  of  avian  bone.  The  length  of  the  skull  be- 
hind the  fronto-nasal  suture  is  2  inches  5  lines ;  and  from  the  pro- 
portions of  the  frtigment  of  the  upper  mandible  preserved,  the  author 
concluded  that  the  total  length  of  the  perfect  skull  could  not  be  less 
than  between  5  and  6  inches.  The  author  proceeded  to  compare 
the  fossil,  which  he  declared  to  present  strictly  avian  characters, 
with  those  groups  of  birds  in  whidi  the  beak  is  longer  than  the  true 
cranium,  a  character  which  occurs  as  a  rule  in  the  Aves  aquaiiecB, 
He  stated  that  none  of  the  Waders  have  the  nostrils  so  remote  from 
the  orbits  as  in  Odoniopteryx ;  and  this  character,  with  the  absence 
of  the  superorbital  gland-pit,  limits  the  comparison  to  the  Totipal- 
mates  and  Lamellirostrals.  The  former  are  excluded  by  their  not 
having  the  orbit  bounded  by  a  hind  wall  as  in  OdontopUryx ;  and  in 
this  and  other  peculiarities  the  fossil  seems  to  approach  most  nearly 


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74  Geotogical  Sociefy: — 

to  the  Attatid»,  in  the  aear  alUeB  of  which,  the  Gkweanden  and  Mer- 
gansers, the  beak  is  fonushed  with  strong  pointed  denticnlations. 
In  these,  however,  the  tooth-like  processes  bdong  to  the  homy  bill 
only ;  and  the  author  stated  that  the  production  of  die  alveolar  margin 
into  bony  teeth  is  peculiar,  so  fiur  as  he  knows,  to  Odnntopteryx, 
He  condiuded,  finom  the  consideration  of  all  its  characters,  ''  that 
Odontopteryx  was  a  warm-blooded,  feathered  bqied,  with  wings ; 
and  further,  that  it  was  web-footed  and  a  fish-eater,  and  that  in  the 
catching  of  its  slii^>ery  prey  it  was  assisted  by  this  pterosanroid 
armature  of  its  jaws."  In  oondusion,  the  author  indicated  the  dia- 
factors  separating  Odawtopteryx  from  the  Cretaceous  fossil  sknll 
lately  described  by  Prof.  0.  G.  Manh,  and  which  he  affirms  to  have 
small,  similar  teeth  implanted  in  distinct  sockets. 

3.  "  Contribution  to  the  Anatomy  of  Hypsihphodon  fbxii,  an 
Account  of  some  recently  acquired  Remains  of  this  Dinosaur."  By 
J.  W.  Hulke,  Esq.,  F.R.8.,  F.G.8. 

After  referring  to  Professors  Owen  and  Huxley's  descriptions  of 
the  Mantell-Bowerbank  skeleton  in  the  British  Museum,  and  to  tiie 
paper  by  the  last-named  gentleman  on  the  skull  of  this  Dinosaur 
read  at  a  meeting  of  this  Society  in  1 870,  the  author  communicated 
details  of  its  dentition,  the  form  of  its  mandible,  and  that  of  the 
cones  of  the  shoulder  and  fore  limb,  and  of  the  haunch  and  hind 
limb,  hitherto  imperfectly  or  quite  unknown.  The  resemblance  to 
Igwmodon  is  greater  than  had  been  supposed ;  but  the  generic  di- 
stinctness of  HypsUcjphodon  holds  good. 

4.  <<  On  the  Glacial  Phenomena  of  the  '  Long  Mand,'  or  Outer  He- 
brides." By  James  Geikie,  Esq.,  F.R.S.E.,  F.GJ3.,  of  H.M.  Geolo- 
gical Survey  of  Scotland. — First  piqper. 

The  author  commenced  by  describing  the  physical  features  of 
Lewis,  which  he  stated  to  be  broken  and  mountainous  in  the  south, 
whilst  the  north  might  be  described  as  a  great  peat  moss  rising 
gradually  to  a  height  of  about  400  feet,  but  with  the  rock  breaking 
through  here  and  there,  and  sometimes  reaching  a  higher  elevation. 
The  north-east  and  north-west  coasts  are  comparatively  unbroken ; 
but  south  of  Aird  Laimisheadar  in  the  west  and  Stomoway  in  the 
east,  many  inlets  run  far  into  the  country.  The  island  contains  a 
great  number  of  lakes  of  various  sizes,  which  are  most  abundant  in 
the  southern  mountain  tract  and  in  the  undulating  ground  at  its 
base.  The  greater  part  of  Lewis  consists  of  gneiss,  the  only  other 
rocks  met  with  being  granite  and  red  sandstone,  and  conglomerate 
of  Cambrian  age.  The  stratification  of  the  gneissic  rocks  is  generally 
well-marked ;  the  prevalent  strike  is  N.E.  and  8.W.,  with  S.E.  dip, 
generally  at  a  high  angle.  The  author  described  in  considerable 
detail  the  traces  of  glaciation  observed  in  the  lower  northern  part  of 
Lewis,  and  inferred  from  his  observations  that  the  ice  passed  from 
sea  to  sea  across  the  whole  breadth  of  this  district,  and  that  it  not 
only  did  not  come  from  the  mountainous  tract  to  the  south,  but  must 
have  been  of  sufficient  thickness  to  keep  on  its  course  towards  the 
north-west  undisturbed  by  the  pressure  of  the  glacier  masses  which 
must  at  the  same  time  have  filled  the  glens  and  valleys  of  that 


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Mr»  Campbell  on  the  Okdal  Phenomena  of  the  Hebrides.    76 

nMmQteb^egion.  After  deeoribing  the  ohareoten  prsBented  by  the 
bottom-till  in  the  northern  part  ^  Lewis,  the  antiior  proceeded  to 
notice  those  of  the  lakes,  wane  of  whieh  toend  nortii-weet  and  south- 
east, others  north-east  and  sonth-west,  irfailsl  those  <^  the  mountain 
district  follow  no  particolar  direction.  The  lake-basins  of  the  first 
seiies  he  regarded  as  fonned  at  the  same  time  and  by  the  same 
agency  as  the  roehee  mouionnies  and  other  marks  of  glacial  action ; 
jthey  are  tme  rock-basins  or  hollows  between  paiallel  banks  formed 
whoJly  of  till,  or  of  till  and  rock.  The  N  JB.  and  S.W.  lakes  coin- 
cide in  direetion  precisely  with  the  strike  of  the  gneiss ;  and  the 
anyior  explained  their  origin  by  the  deposition  of  till  by  the  land-ice 
in  passing  over  the  escaipments  of  tiie  gneiss  facing  the  nortii-west. 
Hie  lakes  of  the  mountain  district  are  regarded  by  the  author  as  all 
prodneed  by  glacial  erosion.  The  auth^  considered  ^t  the  ice 
which  passed  over  the  northern  part  of  Lewis  could  only  have  come 
from  tiie  mainland.  Beferring  to  the  glaciation  of  Eaasay,  he 
showed  that  the  ice-sheet  which  effected  it  must  have  had  in  the 
Jnner  Sound  a  deftth  of  at  least  2700  feet ;  and  taking  this  as  ap- 
proximately Uie  thickness  of  the  mer  de  glace  which  flowed  into  the 
Minch,  which  is  only  between  50  and  60  fathoms  in  depth,  no  part 
of  this  ice  could  have  floated,  and  the  mass  must  have  pressed  on 
over  the  sea-bottom  just  as  if  it  had  been  a  land  suiiiace.  Lse 
coming  from  Butherland  must  have  {urevented  the  flow  of  the  Boss- 
shire  ice  through  the  Minch  into  the  North  Atlantic,  and  forced  it 
over  the  low  northern  part  of  Lewis ;  and  the  height  to  which  Lewis 
has  been  glaciated  seems  to  show  that  the  great  ioe^heet  continued 
its  progress  until  it  reached  the  edge  of  the  100-fathom  plateau,  40 
or  50  miles  beyond  the  Outer  Hebrides,  and  then  gave  off  its  ice- 
bergs in  the  deep  waters  of  the  Atlantic. 

5.  *'  Notes  on  the  Glacial  Phenomena  of  the  Hebrides."  By  J. 
F.  Campbell,  Esq.,  F.G.S. 

This  communication  consisted  of  notes  extracted  from  the  author's 
journal,  giviog  his  observations  of  indications  of  glacial  action  in 
various  idands  of  the  group  of  the  Hebrides.  Heynish  in  Tiree  is 
500  feet  high,  and  has  many  large  perched  blocks  on  its  top.  These 
blocks  are  <^  gneiss ;  and  the  author  thought  they  came  from  the 
north-west  The  Barra  islands  are  described  as  rocky,  and  resem- 
bling the  hill-tops  of  a  submerged  land.  All  ice-marks  found  by  the 
author  seemed  to  him  to  come  from  t^e  north  and  west.  He  thought 
that  the  final  grinding  was  given  by  floating  ice  when  the  land  was 
more  submerged  than  at  present.  At  Castle  Bay,  in  Barra,  the  au- 
thor observed  well-preserved  glacial  strise  at  the  sea-level  in  a  direc- 
tion from  N.N.W.  The  whole  island  is  glaciated  and  strewn  with 
perched  blocks.  Glacial  indications  were  also  observed  in  South  Uist, 
B^ibecula,  and  Skye ;  and  the  aitthor  stated  that,  on  the  whole,  he 
was  inclined  to  think  that  the  last  glacial  period  was  marine,  and 
that  heavy  ice  came  in  from  the  ocean,  the  local  conditions  being 
like  those  of  Labrador.  The  author  regarded  most  of  the  l^e- 
basins  of  the  Hebrides  as  formed  by  ice-action,  and  considered  that 
the  ice  by  which  those  islands  were  glaciated  came  from  Greenland. 


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76  Geological  SocUly. 

6.  *'  On  Fossil  Corals  from  the  Eocene  Formation  of  the  West 
Indies."    By  Prof.  P.  Martin  Duncan,  M.B.,  F.R.S.,  V.P.G.8. 

The  author  had  considered  his  lahours  amongst  the  fossil  corals  of 
the  West-Indian  Islands  finished ;  hut  lately  a  yery  fine  collection  has 
heen  sent  to  him  from  the  Unirersity  of  Upsala,  and  Mr.  P.  T.  Clere 
of  Stockholm.  The  specimens  were  collected  from  limestone  and  coral 
conglomerates,  which  are  covered  by  and  rest  upon  ydoanic  d^ris 
and  ejectamenta  in  the  Island  of  St.  Bartholomew.  The  species  re- 
presented there  are  numerous,  and  may  he  divided  into :— ^roup  1, 
species  not  hitherto  known ;  2,  species  with  a  Cretaceous  fades ; 
3,  species  characteristic  of  the  horizons  of  the  Upper  Eocene  and 
Oligocene  deposits  of  Europe ;  4,  species  found  also  in  the  Nummu- 
Utic  deposits  of  Europe  and  Sinde;  5,  species  belonging  to  the 
recent  coral  fauna ;  6,  species  belonging  to  genera  which  belong  to 
the  Jurassic  fauna,  and  to  the  Caribbean. 

The  determination  of  the  forms  of  the  associated  MoUusca  and 
Echinodermata  permit  the  following  deposits  being  placed  on  a 
general  geologic^  horizon — the  limestone  and  conglomerate  of  St 
Bartholomew,  the  dark  shales  beneath  the  Miocene  of  Jamaica, 
the  beds  of  San  Fernando,  Trinidad.  These  were  probably  contem- 
poraneous with  the  Java  deposits,  the  Eocene  of  the  Hala  chain, 
the  great  reefs  of  the  Castel  Gomberto  district,  the  reefs  of  Ober* 
berg  in  Steiermark,  and  the  Oligocene  of  Western  Europe. 

The  author  has  already  described  reef  corals  from  the  Lower  Cre* 
taceous  (Upper  Greensand)  of  Jamaica ;  and  the  size  of  the  sped* 
mens  proves  that  the  reef  was  exposed  to  the  surf  of  an  open  sea. 
To  these  reefis  succeeded  on  the  same  area  others  in  the  Eocene 
time,  in  the  Miocene  and  Pliocene ;  and  there  are  modem  reefis  in 
the  neighbourhood. 

The  affinities  and  identities  of  the  fossil  forms  with  those  of  con- 
temporaneous reefs  in  Asia  and  Europe,  and  the  limitation  of  the 
spedes  of  the  existing  Caribbean  coral  fauna,  point  out  the  correct- 
ness of  the  views  put  forth  by  8.  P.  Woodward,  Carrick  Moore,  and 
the  author,  concerning  the  upheaval  of  the  Isthmus  of  Panama  after 
the  termination  of  the  Miocene  period. 

7.  "  Note  on  the  Lignite-deposit  of  Lal-Lal,  Victoria,  Australia.'' 
By  R.  Etheridge,  Esq.,  Jun.,  F.G.S. 

The  author  described  this  depodt,  which  is  worked  at  the  village 
of  Lal-Lal,  south  of  Mount  Bunniyong.  A  boring  towards  the  centre 
of  the  deposit  showed  about  73  feet  of  sand,  day,  and  gravel,  3  feet 
of  fireday,  and  1 15  feet  of  lignite.  The  lignite  is  an  earthy  bitu- 
minous coal,  composed  of  branches,  roots,  &c.  of  coniferous  trees. 
In  the  mass  there  are  a  few  thin  seams  of  jet  and  day-beds,  accom- 
panied by  two  kinds  of  resin.  The  lignite  is  very  poor  in  carbon. 
It  is  almost  entirely  composed  of  remains  of  coniferous  plants  not 
now  existing  in  Victoria ;  and  the  author  conddered  that  it  is  nearly 
of  the  same  age  as  the  Lignite  depodt  of  Morrison's  Diggings,  whidi 
has  been  regarded  as  Miocene. 


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C     77     ] 
XII.  IntelUgenee  and  Migcellaneau$  Articles. 

ON  THB  FLOW  OF  SALINE  SOLUTIONS  THROUGH  CAPILLARY  TUBB8. 
BT  THEODORE  HUBfiNER. 

rPHE  velocity  of  the  flow  of  solutions  in  capillary  tubes  appears 
^  not  to  depend  solely  on  their  weight  and  capillary  adhesion. 
Poiseuille  has  demonstrated  that  the  velocity  of  flow  of  a  mixture  of 
water  and  alcohol  decreases  in  proportion  as  the  specific  gravity 
increases  by  the  addition  of  larger  and  larger  quantities  of  water, 
to  a  Tninimiim  which  corresponcis  exactly  to  the  maTiTnum  of  con- 
traction of  the  mixture.  GKrard  found  that  the  velocity  of  flow  of 
chloride  of  sodium  is  less  than  than  that  of  a  solution  of  chloride 
of  potassium  of  the  same  density. 

M.  Hiibener  thought  that,  beside  the  adhesion  and  the  weight  of 
the  liquid,  an  important  factor  for  the  velocity  of  flow  of  a  solution 
must  be  the  intermolecular  friction  resulting  from  its  greater  or 
less  cohesion ;  and  to  test  this  he  has  compared  the  velocities  of  a 
nomber  of  solutions  of  very  different  chemical  compositions  brought 
to  the  same  density. 

The  liquid  was  introduced  into  a  vertical  rectilinear  glass  tube  of 
50  centims.  length  and  1*78  centim.  diameter,  having  a  capillary 
continuation  of  about  40  centims.  length.  The  large  tube  presented 
two  marks;  and  with  a  seconds-watch  the  time  was  accurately 
measured  which  was  required  for  the  level  of  the  liquid  to  tall  from 
one  of  these  marks  to  the  other. 

Operating  in  this  way  upon  solutions  of  chloride,  bromide,  and 
iodiae  of  potassium,  of  chloride  of  sodium  and  of  ammonium,  with 
a  density  of  1*059  and  at  a  fixed  temperature,  the  author  ascertained 
tiiat  the  velocity  of  flow  of  saline  solutions  is  as  much  lower  as  the 
atomic  weight  of  the  salt  dissolved  is  less.  For  the  different  binary 
bodies  abovein£cated,  it  is  the  metal  which  has  the  greatest  influence 
opon  the  velocity  of  flow,  much  more  than  the  metalloid.  The  va- 
riations presented  by  the  velocity  from  one  body  to  another  are  as 
much  more  marked  as  the  tube  is  more  capiUary  and  as  the  con- 
centration of  the  solution  is  greater. 

On  comparing  two  solutions,  of  chloride  of  sodium  and  potassium, 
at  1*1058  density,  the  author  arrived  at  the  remarkable  result  that 
the  times  of  flow  of  these  two  salts  are  found  to  be  very  sensibly 
proportional  to  their  equivalents.  From  this  experiment,  and  from 
others  fuialogous,  extended  also  to  the  chlorides  of  the  alkaline-eiarthy 
metals  barium,  strontium,  magnesium,  M.  Hiibener  thinks  it  may  be 
concluded  generally  with  a  high  degree  of  probability,  that  the  velo- 
cities of  flow  of  these  bodies  in  solution  in.  water,  to  a  certain  degree  of 
concentration,  are  in  the  same  ratio  as  their  equivalents. 

The  explanation  of  these  facts  is,  according  to  M.  Hiibener, 
to  be  found  in  the  circumstance  that  the  molecules  of  substances 
which  have  a  higher  equivalent  are  larger,  but,  on  the  other  hand, 
in  less  number,  and  consequently  must  give  rise  to  less  friction 
with  the  solvent  in  which  they  ai*e  held,  thus  communicating  greater 


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78  IrUeUigenee  and  Miseellaneoui  Articki. 

mobility  to  the  solution. — BihUaiheque   UniverBsUe,  AreMvu  dtt 
Sciences  Phys.  et  Nat.  No.  197,  pp.  76,  76. 

BY  W.  LOWEET. 

In  performing  Melde'e  experiment  upon  the  vibrations  of 
strings,  it  is  desirable  to  change  the  tension  of  the  vibrating  cord 
in  a  continuous  manner.  The  ordinary  method  of  attaching 
weights  to  the  cord  does  not  admit  of  this  with  precision ;  and  with 
small  weights  the  movement  of  the  weight  itself,  on  account  of  the 
rapid  vibration  of  the  string,  prevents  the  formation  of  the  ventral 
segments  with  regularity.  I  have  adopted  the  following  method : — 
A  glass  tube  graduated  into  millimetres  is  weighted  so  as  to  float 
in  a  vertical  position:  this  is  attached  to  the  silk  cord  whidi 
hangs  from  the  prong  of  the  tuning-fork,  and  is  placed  in  a  glass 
vessel  filled  with  water.  This  latter  vessel  is  provided  with  a 
siphon,  by  means  of  which  the  water  can  be  drawn  ofF  at  pleasure. 
It  will  be  readily  seen  that,  by  drawing  off  the  water  from  the 
larger  vessel,  the  displacement  produced  by  the  graduated  glass 
tube  is  diminished,  ana  the  tension  of  the  string  thereby  is  increased. 
By  diminishing  or  increasing  the  amount  of  water  in  the  larger 
vessel  the  tension  can  be  diminished  or  increased  to  the  desirod 
extent. 

In  order  to  make  quantitative  experiments,  the  tube  is  in  the  first 
place  connected  with  the  arm  of  a  delicate  hydrostatic  balance. 
The  balance  is  adjusted  when  the  level  of  the  water  in  which  the 
tube  floats  is  at  the  zero  of  the  millimetre  scale.  In  order  to 
avoid  errors  in  reading,  it  is  best  to  use  a  cathetometer.  The 
weights  which  are  necessary  to  keep  the  index  of  the  balance  at 
aero,  when  the  level  of  the  water  in  the  outer  vessel  falls  through 
the  millimetre  divisions  on  the  graduated  tube,  are  noted,  llie 
upward  pressure  of  the  water,  and  consequently  the  tension  upon 
the  suspending  cord,  are  then  given  in  grams. 

In  order  to  show  the  regiuarity  of  the  method,  the  following 
results  of  one  experiment  are  given.  In  the  experiments,  a  glass 
tube  which,  immersed  at  110  millims.  on  the  scale,  weighed  two 
grams  gave,  when  the  level  of  the  water  in  the  outer  vessel  was 
lowered,  the  following : — 

Immersed  at  110  millims.  Weight  «  2  grams. 

102       „  „  2-5  „ 

tf  93'5    „  „  3      „ 

„  S5  ^    „  „  3*6  „ 

»>  76-5    „  „  4     „ 

„  67*6    „  „  4*5  „ 

»»  ®0      „  „  6     „ 

ff  43      „  „  6-6  „ 

In  these  experiments  a  fidl  *of  8*1  millims.  corresponded  to  a 
difference  of  *5  of  a  gram.  It  is  evident  by  increasing  the  sise  of 
the  outer  vessel  that  a  large  amount  of  water  would  measure  a 
slight  displacement.  When  the  cord  was  set  in  vibration,  the  fol- 
lowing results  were  obtained  : — 


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TntelUgenee  and  Miscettaneaus  Articles.  79 

Paint  Wmgfate 

of  immenion.  in  grams.  yibrations. 

110  2  6 

84  3-5  6 

76  4  4 

30  6-7  3 

The  ratio  of  the  numbers  in  the  second  and  third  columns  will  be 
found  to  follow  Melde's  law. 

For  qualitative  or  quantitative  experiments  upon  beats  or  Lissa- 
jous  curves  this  method  of  loading  the  prong  of  a  tuning-fork  can 
advantageously  replace  the  bit  of  wax  or  the  sliding  weight,  since 
we  have  at  our  command  a  quick  and  precise  method  of  adjustment. 
— Silliman's  American  Joumaly  May  1874. 

ON  CONSTANT  ELECTRIC  CURRENTS.      BY  M.  HEINE^  OP  HALLE. 

Kirchhoff*  has  developed  a  simple  expression  for  the  elebtric 

Potential,  with  a  constant  current,  in  every  point  P  of  a  circular 
omogeneous  plate  into  which  the  current  enters  at  given  points 

Aj,  A^, If  each  letter  E  represents  a  constant  depending  on 

the  strength  of  the  current  entering  at  the  point  A„  and  if  B^  is 
the  conjugate  point  to  A^,  the  electric  potential  of  the  circle  in  the 
point  P  becomes 

V=2E,log(PA,.PBJ,    (a) 

when  the  summation  is  extended  to  all  the  points  of  inflow.  Two 
points  A,  B  of  the  circle  are  called  conjugate  which  lie  on  the  same 
right  line  M AB  starting  from  the  centre  M,  if  the  radius  forms  the 
mean  proportional  between  MA  and  MB. 

I  have  found  the  expression  of  the  potential  also  for  plates  of 
other  shapes,  and  will  here  give  it  for  the  ellipse  and  the  rectangle. 
Let  the  excentridty  of  the  ellipse  be  1 ;  let  the  fourth  power  of 
ihe  difference  of  the  semiaxes  (oi  which  the  greater  represents  the 
axis  of  the  real,  the  smaller  that  of  the  imaginary)  be  put  =sq. 
Let  each  point  z  of  the  ellipse  be  described  by  the  elliptic  function 

/2K         .     \ 
$nl  —  arc  sin  z  j, 

therefore  the  entire  ellipse  upon  a  circle  with  the  radius  -j^  (as  M. 

Sdiwarz  has  shown).  If  now  a,  p  are  the  images  of  the  inflow- 
points  A  and  an  arbitrary  point  P  of  the  ellipse,  and  if  h  denotes 

the  point  in  the  circle  of  radius  —t=.  conjugate  to  a,  the  electric  po- 

tential  of  the  ellipse  in  the  point  P  will  be 

V«SE'log(pa..i>5j (/3) 

If,  lastly,  we  have  a  rectangle  OXNY,  whose  base  OX  has  the 
leneth  w  and  is  the  axis  of  the  real,  and  its  height  OY  equals 
—  log  ^  and  is  the  axis  of  the  imaffinary,  we  construct  for  each 
point  ot  inflow  A  the  three  reflected  images  B,  G,  D  which  arise 
when  A  is  assumed  to  be  luminous,  OX  and  OY  reflecting  (^-l:y», 
«— y»,  — ^— y»,  — ^-fy*)*  I^  ^^^  ®*<5h  point  z  be  represented  by 
♦  Pogg.  Aim.  vol.  Ixiv.  p.  497,  v<^.  Ixvit.  p.  344. 


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80  Intelligence  and  Miicellaneoui  Art%ele$. 

«n*  — ,  and  thereby  A,  B,  C,  D,  and  the  arbitrary  point  P  of  the 

IT 

rectangle  fall  upon  points  a,  5,  c^  d,  p,  the  electric  potential  of  the 
rectangle  in  the  point  P  is 

V=5  E,  log  (pa,  .pb,  .pc,  .pd,). (y) 

Quincke*  bases  his  experiments,  on  the  potential  in  very  large 
square  plates  when  the  points  of  inflow  are  in  the  diagonal,  upon 
a  formiila  of  approximation  which  in  our  notation  would  be 

V=?  E,  log  (PA, .  PB, .  PC, .  PDJ. 
It  is  now  apparent,  if  this  be  compared  with  the  exact  formula  (y\ 
that  it  results  from  the  latter,  if  $nz  may  be  supposed  propor- 
tional to  z,  therefore  with  very  large  rectangular  plates — or,  betttf , 
under  the  supposition  that  P  and  the  A's  lie  near  an  angular 
point  of  the  rectangle.  The  approximation-formula  therefore  holds 
also  when  the  rectangle  is  not  a  square  and  when  the  inflow-points 
do  not  lie  on  the  diagonal. 

The  derivation  of  these  expressions  I  intend  to  communicate,  in 
a  connected  form,  to  Borchardt's  Journal  fur  Mathematik.  For 
this  reason  I  omit  here  the  exhibition  in  a  purely  analytical  form, 
without  the  aid  of  geometry,  of  the  relations  expressed  by  (/3)  and 
(y). — Monatsherieht  der  honiglich  preussischen  Akademie  der  Wia- 
senseh,  zu  Berlin,  March  6,  1874. 


ON  THE  NATUEE  OF  THE  ACTION  OP   LIGHT    UPON   SILVER    BRO- 
MIDE.     BT  H.  CAREY  LEA,  PHILADELPHIA. 

When  silver  bromide  is  exposed  for  a  moment  to  light,  it  under- 
goes no  visible  change,  but  has  acquired  the  property  of  passing  to 
an  intense  black  when  treated  with  p3rrogallic  add  and  an  alkaU. 

As  to  the  nature  of  this  black  substance,  there  has  existed  con- 
siderable diversity  of  opinion.  In  a  paper  published  on  the  subject 
about  a  year  since  by  Captain  Abney,  F.C.S.,  he  expressed  the 
opinion  that  it  was  an  oxide  of  silver. 

Some  years  since,  while  investigating  the  action  of  light  upon 
silver  iodide,  I  succeeded  in  provins;  that  the  black  substuice 
which  is  produced  when  silver  iodide  is  exposed  to  light  in  presence 
of  silver  nitrate  contains  iodine,  and  is  therefore  either  a  sub- 
iodide  or  an  oxy-iodide.  The  quantity  obtained  was  too  small  to 
enable  me  to  ascertain  which.  When  this  black  substance  was 
treated  with  nitric  acid,  normal  yellow  silver  iodide  was  left  behind, 
and  silver  was  found  on  solution. 

I  have  recently  applied  the  same  treatment  to  the  bromine  com- 
poimd  with  similar  results.  I  And  that  when  silver  bromide  is 
treated  with  pyrogallic  acid  and  alkali  after  exposure  to  light,  the 
black  substance  which  remains  contains  bromine,  and  is  resolved  by 
nitric  add  into  normal  silver  bromide  (left  behind  as  a  pale  yellow 
film)  and  silver,  which  passes  into  solution.  It  is  therefore  either 
a  subbromide  or  an  oxy-oromide,  not  an  oxide,  probably  the  former. 

The  existence  of  these  compounds  is  evidently  an  argument  for 
doubling  the  atomic  weight  of  lUver,  as  has  recently  been  proposed 
on  other  grounds. — SilHman's  Am&riean  Journal^  May  1874. 
*  Pogg.  Ann,  vol.  xcvii.  p.  382. 


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I' 
I 


4 

1^ 


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THE 
LONDON,  EDINBURGH,  and  DUBLIN 

PHILOSOPHICAL    MAGAZINE 

AND 

JOURNAL   OF   SCIENCE, 


[FOURTH  SERIES.] 


AUGUST  1874. 


XIII.  On  Attraction  and  Repulsion  accompanyirw  Radiation^ 

By  William  Crookes,  F.U.S.  ^c.*^ 

[With  a  Plate.] 

BEFORE  describing  the  apparatus  and  experiments  which 
illustrate  the  attraction  and  repulsion  accompanying  ra- 
diation^ it  will  perhaps  be  best  to  draw  attention  to  the  modifi- 
cation of  the  Sprengel  pump  which  has  so  materially  assisted 
me  in  this  investigation. 

Fig.  1  (Plate  I.)  shows  the  pump  as  now  in  use.  Working 
so  much  with  this  instrument^  I  have  endeavoured  to  avoid  the 
inconveniences  attending  the  usual  mode  of  raising  mercury 
from  the  lower  to  the  upper  reservoir.  The  mercuiy  is  con- 
tained in  a  closed  glass  reservoir  A^  perforated  with  a  fine  hole 
at  the  top.  This  reservoir  is  attached  to  a  block  capable  of  free 
movement  in  a  vertical  line  and  running  in  grooves,  and  con^ 
nected  with  the  lower  resei*voir  by  a  flexible  tube  g.  This  tubing 
is  specially  made  to  stand  a  considerable  pressure  of  mercury. 
It  consists  of  a  double  thickness  of  india-rubber  tubing  enclosing 
a  canvas  tube  in  the  centre,  the  whole  being  vulcanized  together. 

When  the  whole  of  the  mercury  has  run  through  the  pump, 
the  reservoir  and  slide  can  be  lowered  by  liberating  a  detent,  T, 
and  letting  it  descend  to  the  block  L.  H  is  a  glass  reservoir 
which  receives  the  mercury  after  flowing  through  the  pump. 
When  the  reservoir  A  is  emptied  and  has  been  lowered  to  the 
block  L,  the  mercury  from  H  is  admitted  into  A  by  opening 
ihe  tap  I.  At/  is  another  tap,  of  platinum,  to  regulate  the  flow 
of  mercury  through  the  pump,     c,  c,  d  are  mercury  joints,  it 

*  A  Lecture  delivered  before  the  Physical  Society,  June  20, 1874.  Com- 
municated by  the  Societv. 

Phil.  Mag.  S.  4.  Vol.  48.  No.  Z\Q.  Aug.  1874.  G 


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82  Mr,  W.  Crooke«  on  Attraclion  and 

being  inconvenient  to  have  the  apparatus  in  one  piece  of  tubing, 
and  not  always  possible  to  seal  the  different  portions  together 
by  fusion.  « «  is  a  barometer  dipping  into  the  same  vessel  as 
the  gauge-barometer  P>  the  two  thus  forming  a  differential 
system  by  which  the  rarity  of  the  atmosphere  in  the  apparatus 
undergoing  exhaustion  can  be  easily  estimated,  dd  is  a  milli- 
metre-scale with  pointed  end,  attached  to  the  gauge  and  capable 
of  being  raised  or  lowered  so  as  to  make  the  point  just  touch 
the  surface  of  the  mercury,  i  is  a  reservoir  of  strong  sulphuric 
acid,  exposing  as  much  surface  as  possible,  but  allowing  the  air 
to  pass  across  it  without  resistance.  The  mercury  joint  (f  may 
either  be  closed  with  a  piece  of  glass  rod  ground  in,  or  it  may  have 
either  of  the  two  pieces  of  apparatus  t  and  k  fitted  to  it.  A  is  a 
mercurial  siphon  gauge,  which  is  useful  for  measuring  very  high 
rarefactions  in  experiments  where  difference  of  pressure  equal 
to  a  tenth  of  a  millimetre  of  mercury  is  impoitant.  t  is  for  still 
higher  rarefactions ;  it  is  simply  a  small  tube  having  platinum 
wires  sealed  in,  and  intended  to  be  attached  to  an  induction- 
coil.  At  exhaustions  beyond  the  capabilities  of  the  mercurial 
gauge  I  can  still  get  valuable  indications  of  the  nearness  to  a 
perfect  vacuum  by  the  resistance  of  this  tube.  I  have  frequentlv 
carried  exhaustion  to  such  a  point  that  an  induction-spark  will 
not  strike  across  the  small  distance  {\  inch)  separating  the  wires 
of  the  vacuum-tube,  h  is  the  mercury-tap  usually  employed  for 
letting  air  into  the  apparatus,  and  also  for  moistening  the  inte- 
rior of  the  pump  with  oil  of  vitriol.  /  is  a  spiral  of  glass  for 
attaching  the  various  pieces  of  apparatus  requiring  exhaustion. 
As  blown  or  fused  joints  are  indispensable,  this  form  of  con- 
necting piece  is  adopted  to  ensure  the  necessary  flexibility, 
m  is  a  trap  to  catch  any  air  which  might  leak  in  through  the 
platinum  tap/,  or  the  various  joints  in  the  lower  part  of  the 
tubing  g. 

The  reservoir  A  being  filled  with  mercury,  the  tap  I  is  turned 
off  and  the  reservoir  is  raised  to  the  top  of  the  slide  where  it  is 
supported  by  the  detent  T.  On  opening  the  tap /the  mercury 
rises  in  the  tube /A,  and,  falling  through  the  chamber  N,  carries 
with  it  the  air  contained  in  the  tube  R,  and  in  the  apparatus 
attached  to  the  tube  /,  as  in  the  ordinarv  Sprengel  pump.  At  N 
the  tubing  is  enlarged  in  order  that  the  mercury  may  not  be 
forced  up  the  tube  R,  as  otherwise  frequently  happens  if  the 
tubes  or  the  mercurv  gets  soiled. 

J,  J  are  iron  brackets  supporting  tie  apparatus.  S  is  a  large 
inverted  glass  receiver,  to  collect  the  small  portions  of  mercury 
which  are  unavoidably  and  constantly  being  spilled;  it  should 
contain  a  little  weak  alkaline  solution. 

The  part  of  the  tubing  g,f,  A,  N  forms  a  barometric  siphon 


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Repulsion  accompanying  Radiation.  88 

arrBBgement,  which  effectually  prevenU  air  getting  into  the 
pump  from  the  reservoir  A  when  the  mercury  has  comphjtely 
run  out.  In  this  case  no  harm  whatever  is  done  to  the  opera- 
tion :  the  vacuum  is  not  injured ;  and  the  exhaustion  proceeds 
immediately  on  retransferring  the  mercury  from  the  reservoir  H 
to  the  reservoir  A^  and  raising  A  again  into  its  place.  The  ap- 
paratus, as  thus  aiTsnged^  is  readily  manageable  with  certainty 
of  obtaining  a  barometric  vacuum. 

The  mercury  fall-tube  of  a  pump  in  constant  use  frequently 
wants  cleaning.  I  find  the  most  effectual  means  of  doing  this 
is  to  put  oil  of  vitriol  into  the  funnel  h,  and  then^  by  slightly 
loosening  the  glass  stopper^  allow  a  little  of  the  strong  acid  to 
be  carried  down  the  tube  with  the  mercaiy.  With  care  this 
can  be  effected  without  interfering  with  the  progress  of  eihaus«> 
tion.  The  residual  acid  adhering  to  the  walls  of  the  chamber 
N  does  good  rather  than  harm.  When  sufficient  sulpbnrio  acid 
has  run  into  the  fall-tube,  the  funnel-stopper  can  be. perfectly 
closed  by  pressing  it  in  with  a  slight  twist  and  then  filling  up 
with  mercury. 

Many  physicists  have  worked  on  the  subject  of  attraction  and 
repulsion  by  heat.  In  1792  the  Bev.  A.  Bennet  recorded  the  fact 
that  a  light  substance  delicately  suspended  in  air  was  attracted 
by  warm  bodies;  this  he  ascribed  to  air-currents.  When^  by 
means  of  a  lens,  light  was  focused  on  one  end  of  a  delicately  sus- 
pended arm,  either  in  air  or  in  an  exhausted  receiver,  no  motion 
could  be  perceived  distinguishable  from  the  effects  of  heat. 
After  Mr.  Bennet  the  subject  has  been  more  or  less  noticed 
by  Laplace,  libri,  Fresnel,  Saigey,  Forbes,  Baden  Powell,  and 
Faye ;  but  the  results  have  been  unsatisfactory  and  contradictory. 

My  first  experiments  were  performed  with  apparatus  made  on 
the  principle  of  the  balance.  An  exceedingly  fine  and  light  arm 
is  delicately  suspended  in  a  glass  tube  by  a  double-pointed 
needle ;  and  at  the  ends  are  affixed  balls  of  various  materials. 
Amongst  the  substances  thus  experimented  on  I  may  mention 
pith,  glass,  charcoal,  wood,  ivory,  cork,  selenium,  platinum, 
silver,  aluminium,  magnesium,  and  various  other  metals.  The 
beam  is  usually  either  of  glass  or  straw. 

The  apparatus,  consisting  of  a  straw  beam  and  pith-ball  endS| 
being  fitted  up  as  here  shown  attached  to  the  pump,  and  the 
whole  being  full  of  air  to  begin  with,  I  pass  a  spirit-lamp  across 
the  upper  part  of  the  tube  just  over  one  of  the  pith-balls.  The 
ball  rises.  The  same  effect  is  produced  when  a  bulb  of  hot  water, 
or  even  the  warm  finger  is  placed  over  the  pith-ball. 

On  working  the  pump  and  repeating  the  experiment,  the 
attraction  to  the  hot  body  gets  less  and  less,  until  it  becomes  nily 
and  after  a  certain  barometric  pressure  is  passed,  the  attractiou 

G2 

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81  Mr.  W.  Crookea  on  Attraction  and 

gives  place  to  repulsion^  which  gets  stronger  and  stronger  as  the 
vacuam  approaches  perfection. 

In  order  to  illustrate  more  strikingly  the  influence  exerted  by 
a  trace  of  residual  air,  an  apparatus  (fig.  2)  is  here  shown  in 
which  the  source  of  heat  (a  platinum  spiral,  a,  rendered  incan- 
descent by  electricity)  is  inside  the  glass  tube  instead  of  out- 
side it  as  before.  A  mass  of  magnesium,  i,  turned  conical,  is 
suspended  in  a  glass  tube,  c  J«,  by  a  fine  platinum  wire  of  such 
a  length  as  to  vibrate  seconds.  The  upper  end  of  the  platinum 
wire  is  sealed  into  the  glass  at «,  and  passes  through  to  the  out^de 
for  the  purpose  of  electrical  experiments.  The  platinum  spiral 
is  arranged  so  that  when  the  pendulum  hangs  free  the  magne- 
sium mass  is  about  \  inch  from  it.  In  air  the  red-hot  spiral 
produces  decided  attraction  on  the  magnesium ;  and  by  properly 
timing  the  contacts  with  the  battery,  a  considerable  swing  can 
be  acci^mulated.  On  perfectly  exhausting  the  apparatus,  how- 
ever, tha^  incandescent  spiral  is  found  to  energetically  repel, 
and  a  very  few  contacts  and  breaks  properly  timed  are  suffi- 
cient to  get  up  the  full  swing  the  pendulum  is  capable  of. 

A  siiMpler  form  of  the  apparatus  for  exhibiting  the  phenomena 
of  attraction  in  air  and  repulsion  in  a  vacuum  consists  of  a  long 
glass  tube  a  b  (fig.  8)  with  a  globe  c  at  one  end.  A  light  index 
of  glass  with  pith-balls  at  the  ends  d^  e  is  suspended  in  this  globe 
by  means  of  a  cocoon  fibre.  When  the  apparatus  is  full  of  air 
at  ordinary  pressure,  a  ray  of  heat  or  light  falling  on  one  of  the 
pith-balls  gives  a  movement  indicating  attraction. 

When  the  apparatus  is  exhausted  until  the  barometric  gauge 
shows  a  depression  of  12  millims.  below  the  barometer,  neither 
attraction  nor  repukion  results  when  radiant  light  or  heat  falls 
on  the  pith.  When  the  vacuum  is  as  good  as  the  pump  will 
produce,  strong  repulsion  is  shown  when  radiation  is  allowed  to 
fall  on  one  end  of  the  index.  The  heat  of  the  hand,  or  even  of 
the  body  several  feet  ofl^,  is  quite  sufficient.  The  action  is  in 
proportion  to  the  surface  acted  on  rather  than  to  the  mass. 

The  barometric  position  of  the  neutral  point  dividing  attrac* 
tion  from  repulsion  varies  with  the  density  of  the  mass  on  which 
radiation  falls,  on  the  ratio  of  its  mass  to  its  surface,  and  in  a 
less  degree  on  the  intensity  of  radiation.  In  the  case  of  pith  it 
is  seen  to  lie  at  about  12  millims.  below  a  barometric  vacuum, 
whilst  with  a  heavy  metal  it  is  within  a  tenth  of  a  millim.  of  a 
vacuum.  Experiments  to  try  to  determine  the  law  governing 
the  position  of  the  neutral  point  are  now  in  progress. 

Ice,  or  a  cold  substance,  produces  the  opposite  effects  to  heat. 
Thus  a  bar  of  pith  suspended  in  a  vacuum  is  energetically  re- 
pelled by  the  warm  hand,  whilst  it  is  as  strongly  attracted  by  a 
piece  of  ice.    Cold  being  simply  negative  heat^  it  is  not  easy  at 


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Repulsion  accompanying  Radiation.  85 

first  sigbt  to  understand  how  it  can  produce  attraction.  The 
law  of  exchanges,  however,  explains  this  perfectly.  The  pith 
index  and  the  whole  of  the  surrounding  bodies  are  incessantly 
exchanging  heat-ra^s ;  and  under  ordinary  circumstances  the 
income  and  expenditure  of  heat  are  in  equilibrium.  A  piece  of 
ice  brought  near  one  end  of  the  index  cuts  offthe  influx  of  heat 
to  it  from  that  side,  and  therefore  allows  an  excess  of  heat  to 
fall  upon  it  from  the  opposite  side.  Attraction  by  a  cold  body 
is  thus  seen  to  be  only  repulsion  by  the  radiation  from  the  op- 
posite side  of  the  i*oom. 

Instruments  of  the  kind  just  described  are  perhaps  the  best 
for  exhibiting  large  and  striking  movements  of  attraction  or 
repulsion.  Two  glass  globes  4  inches  in  diameter,  fitted  up  with 
bars  of  pith  3^  x  ^  inch,  are  now  before  you.  One  is  full  of  air 
at  ordinary  pressure,  whilst  the  other  is  completely  exhausted. 
A  touch  with  a  finger  on  a  part  of  the  globe  near  one  extremity 
of  the  pith  will  drive  the  bar  round  over  90^,  in  the  vacuum. 
In  air  the  attraction  is  not  quite  so  strong. 

If  I  place  a  lighted  candle  an  inch  or  two  from  the  vacuous 
globe,  the  pith  bar  commences  to  oscillate.  The  swing  gradu- 
ally increases  in  amplitude  until  one  or  two  complete  revolu- 
tions ar»  made.  The  toraion  of  the  suspending  fibre  here  inter- 
feres, and  the  vibrations  pi*oceed  in  the  opposite  direction.  The 
movement  continues  as  long  as  the  candle  burns*  This  con- 
tinued movement  ceases  if  the  source  of  radiation  is  removed 
some  distance  off;  the  pith  index  then  sets  equatorially.  The 
cause  of  the  continued  vibration  when  the  radiant  body  is 
at  a  particular  distance  from  the  pith  is  easy  to  understand  on 
the  supposition  that  the  movement  is  due  to  the  direct  impact 
of  waves  on  the  suspended  body. 

For  more  accurate  experiments  I  prefer  making  the  apparatus 
differently.  Fig.  4  represents  the  best  form,  ab  is  a,  glass 
tube,  to  which  is  fused  at  right  angles  another,  narrower  tube,  c  d; 
the  vertical  tube  is  slightly  contracted  at  e  so  as  to  prevent  the 
solid  stoper  d,  which  just  fits  the  bore  of  the  tube,  from  falling 
down.  The  lower  end  of  the  stopper  de'iB  drawn  out  to  a  point ; 
and  to  this  is  cemented  a  fine  glass  thread  about  O'OOl  inch 
diameter,  or  less,  according  to  the  torsion  required. 

At  the  lower  end  of  the  glass  thread  an  aluminium  stirrup 
and  a  concave  glass  mirror  are  cemented,  the  stirrup  being  so 
arranged  that  it  will  hold  a  beam  fg  having  masses  of  any  de- 
sired material  at  the  extremities.  At  c  in  the  horizontal  tube 
is  a  plate-glass  window  cemented  on  to  the  tube.  At  &  is  also 
a  piece  of  plate  glass  cemented  on.  Exhaustion  is  effected 
through  a  branch  tube  h  projecting  from  the  side  of  the  upright 
tube.     This  is  sealed  by  fusion  to  the  spiral  tube  of  the  pump, 


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86  Mr,  W.  Crookes  on  Attraction  and 

The  stopper  de^  aad  the  glass  plates  c  and  b^  are  well  fastened 
with  a  cement  of  resin  8  parts  and  bee's- wax  3  parts** 

The  advantage  of  a  glass-thread  suspension  is  that  the  beam 
always  comes  back  to  its  original  position.  Before  jou  is  an 
instrument  of  this  description^  perfectly  exhausted  and  fitted  up 
with  pith  plates  at  each  extremity.  A  ray  of  light  from  the 
electric  lamp  is  thrown  on  to  the  mirror  c,  and  thence  reflected 
on  to  the  opposite  wall.  The  approach  of  a  finger  to  either  extre- 
mity of  the  beam  causes  the  luminous  index  to  travel  several 
feet^  showing  repulsion.  A  piece  of  ice  brought  near  causes  the 
spot  of  light  to  travel  as  much  in  the  opposite  direction. 

Here  is  another  form  of  the  apparatus  (fig.  5).  The  letters 
and  description  are  the  same  as  in  fig.  4^  the  apparatus, 
however^  being  double.  The  pieces  /,  g  on  the  end  of  one 
beam  consist  of  platinum-foil  exposing  a  square  centimetre  of 
surface,  whilst  the  extremities /',y  on  the  other  beam  consist  of 
pith  plates  of  the  same  siec.  It  Las  already  been  explained  that 
the  neutral  point  of  rarefaction  for  platinum  is  much  higher  than 
for  pith ;  conaequently  at  a  pressure  intermediate  between  these 
two  neutral  points,  radiation  ought  to  eause  the  platinum  to 
be  attracted  and  the  pith  to  be  repelled.  This  is  seen  to  be 
the  case.  A  wide  beam  of  radiant  heat  thrown  in  the  centre  of 
the  tube  on  to  the  plates  gyf  causes  g  to  be  attracted  andy  to 
be  repelled^  as  shown  by  the  light  reflected  from  the  mirrors 
Cy  c\  The  atmospheric  pressure  in  the  apparatus  is  equal  to 
about  40  millinos,  of -mercuiy. 

The  position  of  the  neutral  point  not  only  depends  on  the 
density  of  the  body  acted  on  by  radiation^  as  in  the  above  case, 
but  also  on  the  relation  of  surface  to  mass.  Thus  a  square  cen- 
timetre of  thin  platinum-foil  on  the  extremity  of  the  beam 
requires  a  lower  exhaustion  for  neutrality  than  a  thicker  piece 
exposing  the  same  surface.  Also  a  flat  disk  of  platinum  has  a 
lower  neutral  point  than  the  same  weight  of  platinum  in  the 
form  of  a  sphere. 

Intensity  of  radiation  likewise  affects  the  neutral  point.    With 

*  This  is  the  best  cement  I  have  used  for  standing  a  Tncuura :  for  a 
few  hours  it  is  perfect.  But  at  the  highest  exhaustions  it  seems  to  leak  in 
the  course  of  a  day  or  two.  India-rubber  joints  arc  of  no  use  in  these  ex- 
periments, as,  when  the  vacuum  is  near  upon  perfect,  they  allow  oxygenized 
air  to  pass  through  as  readily  as  the  pump  will  remove  it.  Whenever 
possible  the  glass  tubes  should  be  unitca  by  fusion ;  and  where  this  is  im- 
practicable mercury  joints  should  be  used.  The  best  way  to  make  these  is 
to  have  a  well-made  perforated  eonical  stopper,  cut  from  plain  india-rubber, 
^tting  into  the  wide  funnel-tube  of  the  jomt  and  carrying  the  narrow  tube. 
Before  fitting  the  tubes  in  the  india  rubber  this  is  heated  in  a  spirit-lamp 
until  its  surface  is  decomposed  and  vciy  stickv ;  it  is  then  fitted  into  its 
place ;  mcrcurj-  is  poured  over,  and  oil  of  vitriol  on  the  top  of  that.  When 
well  made,  this  joint  seems  p^fect. 


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RepuUion  accompanying  Radiation.  87 

pith  extremities  a  point  of  rarefaction  can  be  obtained  at  which 
the  warm  fingers  repel  and  incandescent  platinum  attracts. 

Baring  the  coarse  of  this  lecture  I  have  spoken  frequently  of 
repalsion  by  heMt^  and  have  used  a  spirit-lamp  as  a  source  of 
h4»t  to  illustrate  the  facts  described.  I  now  wish  to  show  that 
these  results  are  not  confined  to  the  heating  rays  of  the  spec- 
trum,  but  that  any  ray,  from  the  ultra-red  to  the  ultra-violet,  will 
produce  repulsion  in  a  vacuum. 

In  ray  own  laboratory  I  have  used  sunlight,  and  have  experi- 
mented with  a  very  pure  spectrum,  taking  precautions  to  avoid 
any  overlapping  or  difi'usion  of  one  part  of  the  spectrum  with 
another.  Here  I  can  only  use  the  electric  light,  and,  in  order 
to  get  results  visible  at  a  distance,  the  spectrum  cannot  be  very 
long. 

The  spectrum  is  formed  with  one  disulphide-of-carbon  prism, 
and  is  projected  on  to  the  screen  by  a  lens.  Immediately  be* 
hind  the  screen  is  an  exhausted  bulb,  having  a  movable  index 
with  pith  terminals  suspended  with  a  cocoon  fibre  (fig.  3).  This 
is  delicate  enough  to  swing  over  90^  with  a  touch  of  the  finger, 
and  it  will  even  move  under  the  influence  of  a  ray  of  moonlight. 
I  first  of  all  arrange  the  spectrum  so  that  the  extreme  red  would 
fall  on  one  pith  disk  were  it  not  for  the  screen*  On  removing 
the  screen  the  index  immediately  retreats,  making  nearly  half  a 
revolution. 

I  now  replace  the  screen,  and  arrange  the  spectrum  so  that 
the  invisible  ultra-violet  rays  are  in  a  position  to  fall  on  the  pith 
disk.  On  removing  the  screen  the  index  at  once  behaves  as  it 
did  under  the  influence  of  the  red  rays,  and  is  driven  away 
twenty  or  thirty  degrees.  The  action  is  not  so  powerful  as  when 
the  other  end  of  the  spectrum  is  used ;  but  this  may  partly,  if 
not  wholly,  be  accounted  for  by  the  much  greater  concentration 
of  energy  at  the  red  end  of  the  spectrum,  and  expansion  at  the 
violet  end,  when  using  glass  or  disulphide-of-earbon  prisms. 

I  now,  without  disturbing  the  position  of  the  spectrum,  inters 
pose  in  the  path  of  the  rays  a  cell  containing  a  solution  of  iodine 
in  disulphide  of  carbon,  which  is  opaque  to  the  luminous  and 
ultra-violet  rays,  but  transparent  to  the  invisible  heat-rays.  Not 
a  trace  of  repulsion  is  produced.  The  iodine  solution  is  now  re- 
moved and  the  ultra-violet  rays  again  fall  on  the  pith,  producing 
strong  repulsion.  A  thick  screen  of  clear  alum  cut  from  one  of 
Mr.  Spencers  gigantic  crystals  is  now  interposed ;  but  no  efiect 
whatever  is  produced  by  it,  the  ultra-violet  rays  acting  with  un- 
abated energy.  As  alum  cuts  off  all  the  dark  heat-rays,  this 
experiment  and  the  one  before  it  prove  the  suflBcient  purity 
ef  my  spectrum. 

The  spectrum  is  again  turned  iditil  the  dark  ultra-red  heating 


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88  Mr.  W.  Crookes  on  Attraction  and 

rays  fall  on  the  pith.  The  movement  of  repulsion  is  energetic. 
The  iodine  solution,  interposed,  cuts  off  apparently  none  of  the 
Action.  The  alum  plate  cuts  off  a  considerable  amount,  but  by 
no  means  all.  On  uniting  the  alum  and  the  iodine  solution  the 
whole  of  the  spectrum  is  obliterated,  and  no  action  is  produced, 
whatever  be  the  ray  which  would,  were  it  not  for  this  double 
sifting,  fall  on  the  pith. 

Throughout  the  course  of  these  investigations,  which  have 
occupied  much  of  my  spare  time  for  some  years,  I  have  endea- 
voured to  keep  in  my  mind  the  possible  explanations  which  may 
be  given  of  the  actions  observed ;  and  I  have  always  tried,  by 
selecting  some  circumstances  and  excluding  others,  to  put  each 
hypothesis  to  the  test  of  experiment. 

'  The  most  obvious  explanation  is,  that  the  movements  are  due 
to  the  currents  formed  in  the  residual  gas  which  theoretically 
must  be  present  to  some  extent  even  in  those  vacua  which  are 
most  nearly  absolute. 

Another  explanation  is,  that  the  movements  are  due  to  elec- 
tricity developed  on  the  moving  body  or  on  the  glass  apparatus 
by  the  incident  radiation. 

A  third  explanation  has  been  put  forward  by  Professor 
Osborne  Reynolds,  in  a  paper  which  was  read  before  the  Royal 
Society  on  June  18th  last.  He  considers  the  results  to  be  due 
to  evaporation  and  condensation. 

I  will  discuss  these  explanations  in  order. 

First,  the  air-current  theory.  However  strong  may  be  the 
reasons  in  favour  of  this  explanation,  they  are,  I  think,  answered 
irrefragably  by  the  phenomena  themselves.  It  is  most  difficult 
to  believe  that  the  residual  air  in  a  Sprengel  vacuum,  when  the 
gauge  and  barometer  are  level,  can  exert,  when  gently  warmed 
by  the  finger,  an  upward  force  capable  of  instantly  overcoming 
the  inertia  of  a  mass  of  matter  weighing  20  or  30  grains.  It 
must  be  remembered  that  the  upward  current  supposed  to  do 
this  is  simply  due  to  the  diminished  weight  of  a  portion  of  the 
gas  caused  by  its  increase  in  volume  by  the  heat  applied. 

An  air-current  produced  by  heat  may  possibly  cause  the 
beam  of  a  balance  to  rise,  may  drive  a  suspended  index  side- 
ways, and  by  a  liberal  assumption  of  eddies  and  reflections, 
may  perhaps  be  imagined  to  cause  these  movements  to  take 
place  sometimes  in  the  opposite  directions ;  but  as  rarefaction 
proceeds  these  actions  must  certainly  get  less,  and  they  will 
cease  to  be  appreciable  some  time  before  a  vacuum  is  attained : 
a  point  of  no  action  or  neutrality  will  be  reached.  But  this 
neutral  point  should  certainly  be  nearer  to  a  vacuum  when  a 
light  body  like  pith,  exposing  much  surface,  is  under  experiment| 


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Repulsion  accompanying  Radiation.  89. 

than  when  the  mass  acted  on  is  heavy  like  brass ;  whereas  in 
practice  the  contrary  obtains.  Pith  ceases  to  move  under  the 
influence  of  radiation  at  a  rarefaction  of  about  7  to  12  millims., 
whilst  brass  only  ceases  to  be  affected  when  the  gauge  and  ba- 
rometer are  appreciably  level. 

But  even  could  the  phenomena  up  to  the  neutral  point  be 
explained  by  air-currents^  these  are  manifestly  powerless  to  act 
after  this  critical  point  is  passed.  If  a  current  of  air  within  7 
millims.  of  a  vacuum  cannot  move  a  piece  of  pith^  certainly  the 
residual  air  in  a  Sprengel  vacuum  should  not  have  more  power; 
and  a  fortiori  the  residual  gas  in  a  perfect  chemical  vacuum 
cannot  possibly  move  a  mass  of  platinum. 

It  is^  however^  abundantly  demonstrated  that,  in  all  cases  after 
this  critical  point  is  reached^  the  repulsion  by  radiation  is  most 
apparent ;  it  increases  in  energy  as  the  vacuum  approaches  per- 
fection, and  attains  its  maximum  when  there  is  no  air  whatever 
present,  or  at  all  events  not  sufficient  to  permit  the  passage  of 
an  induction-spark. 

I  will  now  refer  to  the  electrical  explanation.  Very  early  in 
my  investigation,  phenomena  were  noticed  which  caused  me  to 
think  that  electricity  played  a  chief  part  in  causing  the  move* 
ments.  When  a  hot  glass  rod  is  held  motionless  against  the 
side  of  an  exhausted  tube  containing  a  pith  index,  repulsion 
takes  place  in  a  perfectly  regular  manner;  but  if  the  glass  rod 
has  been  passed  once  or  twice  through  the  fingers,  or  is  rubbed 
a  few  times  sideways  against  the  exhausted  bulb,  the  index  im- 
mediately moves  about  in  a  very  irregular  manner,  sometimes 
being  repelled  from,  and  at  others  attracted  to,  the  side  of  the 
glass,  where  it  adheres  until  the  electncal  excitement  subsides. 
Friction  with  the  finger  produces  the  same  results;  and  a  small 
spirit-flame  causes  similar,  but  much  fainter,  electrical  effects.  I 
soon  ascertained,  however,  that,  although  electricity  is  capable 
of  producing  many  movements  similar  to  those  caused  by  radia- 
tion, they  are  never  so  alike  as  to  be  mistaken.  Electricity  fre- 
quently interferes  with,  disturbs,  or  neutralizes  the  true  action  of 
radiation ;  but  it  acts  in  such  a  manner  as  to  show  that  it  is  not 
the  primary  cause  of  the  movement.  At  the  highest  rarefactions, 
and  when  special  precautions  have  been  taken  to  avoid  the  pre- 
sence of  aqueous  vapour,  slight  friction  with  the  finger  against 
the  bulb,  or  a  touch  with  the  flame  of  a  spirit-lamp,  excites  so 
much  electrical  disturbance  in  the  pith  and  other  indexes  that 
accurate  observations  become  impossible  with  them  for  several 
hours.  I  have  tried  many  means  of  neutralizing  the  electrical 
disturbance ;  but  they  are  only  partially  successful,  and  at  the 
highest  rarefactions  interference  through  electrification  is  very 
troublesome. 


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90  Mr.  W.  Crookes  on  Attraction  and 

I  miiy  draw  attention  to  the  following  experiments^  which  are 
devised  with  the  objeet  of  showing  that  the  attractions  and  re* 
pulsions  are  not  due  to  electricity. 

In  describing  the  pendulum  apparatus  (fig.  2)  which  I  set  in 
motion  at  the  early  part  of  this  lecture^  I  explained  that  the 
mass  of  magnesium  forming  the  weight  was  in  metallic  con- 
tact with  the  platinum  wire  which  supported  it^  and  that  the 
Upper  end  of  this  platinum  wire  was  fused  into  the  glass  tube 
and  passed  through  to  the  outside.  With  this  apparatus  I  have 
tried  a  great  number  of  experiments.  I  hsTc  connected  the  pro- 
jecting end  of  the  platinum  wire  with  "  earth/'  with  either  pole 
of  an  induction-coil  the  other  being  insulated  more  or  less^  with 
either  pole  of  a  voltaic  battery^  with  a  delicate  electroscope ;  I  have 
charged  it  with  an  electrophorus^  and  have  submitted  it  to  the 
most  varied  electrical  conditions ;  and  stilly  on  allowing  radiation 
to  fall  upon  the  suspended  mass^  I  invariably  obtain  attraction 
when  air  is  present^  and  repulsion  in  a  vacuum.  The  heat  has 
been  applied  both  from  the  outside^  so  as  to  pass  through  the 
glass^  and  also  inside  by  means  of  the  ignited  platinum  wire ; 
and  the  results  have  shown  no  diflFerence  in  kind,  but  only  in 
degree,  under  electrical  excitement.  I  have  obtained  interference 
with  the  usual  phenomena,  but  never  of  such  a  character  as  would 
lead  me  to  imagine  that  the  normal  results  were  due  to  electricity. 

It  occurred  to  me  that  the  repulsion  might  be  due  to  a  deve- 
lopment of  electricity  on  the  inner  surface  of  the  glass  bulb  or 
tube  under  the  influence  of  the  radiation  as  it  passed  from  the 
glass  into  the  vacuum.  This  appears  to  be  disproved  by  the 
fkct  that  the  results  are  exactly  the  same  whether  the  radiation 
passes  through  the  glass,  or  whether  it  is  developed  inside  the 
apparatus  as  in  the  above  instance. 

I  have  produced  exactly  the  same  phenomena  whether  the 
exhausted  apparatus  has  been  standing  insulated  in  the  air,  or 
whether  it  was  completely  immersed  in  water  connected  electri- 
cally with  "  earth,''  or  surrounded  with  wet  blotting-paper. 

Here  are  two  experiments  which  bear  on  this  subject.  A 
straw  beam  furnished  with  brass  balls  at  each  end  is  suspended 
on  a  double-pointed  needle,  and  the  brass  balls  and  needle 
are  placed  in  metallic  connexion  b^  means  of  fine  platinum  wire. 
The  needle  does  not  rest  on  the  sides  of  the  glass  tube,  but  in 
steel  cups,  to  which  is  soldered  a  platinum  wire  passing  through 
the  glass  tube  and  connected  with  ''earth."  The  tube  is  then 
exhausted,  and  the  usual  experiments  are  tried  with  hot  and 
cold  bodies^  both  with  and  without  a  wet  blotting-paper  cover. 
In  all  cases  the  moving  beam  behaves  normally,  being  repelled 
by  heat  and  attracted  l^  cold. 

An  apparatus  is  prepared  similf^r  to  that  shown  in  fig.  4. 


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Repubiott  accompanying  Radiation*  91 

The  inside  of  the  tube  ab  \%  lined  with  a  cylinder  of  copper 
ganse,  having  holes  cut  in  the  centre  for  the  passage  of  the  snp^ 
porting  thread  dc  and  the  index  ray  of  light  felling  on  th« 
mirror  c,  and  holes  at  each  end  to  admit  of  the  plates  /  and  g 
being  experimented  with.  A  wire  attached  to  the  copper  gause 
passes  through  a  hole  in  the  plate  b,  so  as  to  give  me  electrical 
access  to  the  copper  gauae  lining.  Under  the  most  diverse  elec-* 
trical  conditions^  whether  insulated  or  connected  with  ''  earth/' 
this  apparatus  behaves  normally  when  exhausted* 

A  further  reason  why  electricity  is  not  the  cause  of  the  move- 
ments I  have  described  is^  that  they  are  not  only  produced  by 
heat^  but  also  by  ice  and  cold  bodies.  Moreover  1  shall  pi^- 
sently  show  that  any  ray  of  the  spectrum^  besides  those  red  and 
ultra-red  rays  which  produce  dilatation  of  mercury  in  a  thermo- 
meter, excite  an  electric  current  between  antimony  and  bismuth 
couples,  and  cause  a  sensation  of  warmth  when  falling  on  the 
skin,  will  produce  the  effect  of  repulsion  in  a  vacuum.  It  is 
therefore  to  my  mind  abundantly  proved  that  electricity,  such 
as  we  at  present  kuow  this  force^  is  not  a  chief  agent  in  these 
attractions  and  repulsions,  however  much  it  may  sometimes  in- 
terfere with  and  complicate  the  phenomena. 

I  will  now  discuss  Professor  Osborne  Beynolds's  theory,  that 
the  effects  are  the  results  of  evaporation  and  condensation. 
In  my  exhausted  tubes  he  assumes  the  presence  of  aqueous 
vapour,  and  then  argues  as  follows : — "  When  the  radiated  heat 
from  the  lamp  falls  on  the  pith,  its  temperature  will  rise,  and 
any  moisture  on  it  will  begin  to  evaporate  and  to  drive  the  pith 
from  the  lamp.  The  evaporation  will  be  greatest  on  that  ball 
which  is  nearest  to  the  lamp ;  therefore  this  ball  will  be  driven 
away  until  the  force  on  the  other  becomes  equal,  after  which 
the  balls  will  come  to  rest,  unless  momentum  carries  them 
further.  On  the  other  hand,  when  a  piece  of  ice  is  brought 
near,  the  temperature  of  the  pith  will  be  reduced,  and  it  vtill 
condense  the  vapour  and  be  drawn  towards  the  ice." 

Professor  Reynolds  has  tried  an  experiment  with  pith-balls  at- 
tached to  a  light  stem  of  glass  and  suspended  by  a  silk  thread  in  a 
glass  flask.  The  exhaustion  was  obtained  by  boiling  water  in  the 
flask  and  then  corking  it  up  and  allowing  it  to  cool.  The  gauge 
showed  an  exhaustion  of  from  ^  to  |  of  an  inch.  The  pith-balls 
behaved  exactly  as  I  have  already  shown  they  do  at  that  degree  of 
exhaustion,  heat  repelling  and  iee  attracting.  He  found  that  the 
neutral  point  varied  according  to  whether  air  was  present  with 
the  aqueous  vapour,  or  whether  the  vapour  was  pure  water-gas« 
Professor  Reynolds  states  v^^"  From  these  last  two  facts  it  ap- 
pears as  though  a  certain  amount  of  moisture  on  the  balls  was 
necessary  to  render  them  sensitive  to  the  heat.  •  •  •  *  These  ex- 


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92  Mr.  W,  Crookes  on  Attraction  and 

periments  appear  to  show  tbat  evaporation  from  a  surface  is 
attended  with  a  force  tending  to  drive  the  surface  back,  and 
eondensation  with  a  force  tending  to  draw  the  surface  forward/' 

It  does  not  appear  that  Professor  Reynolds  has  tried  more 
than  a  few  experiments ;  and  he  admits  that  they  were  in  reality 
undertaken  to  verify  the  explanation  above  quoted.  I  have 
worked  experimentally  on  this  subject  for  some  years ;  and  the 
last  experiment  recorded  in  my  notebook  is  numbered  584. 
From  the  abundant  data  at  my  disposal,  I  can  find  many  facts 
which  will,  I  think,  convince  you  that  this  hypothesis  has  been 
arrived  at  on  insufficient  evidence. 

In  the  first  place,  I  will  show  that  the  presence  of  moisture  or 
of  a  condensable  vapour  is  not  necessary.  Besides  pith,  which  from 
its  texture  and  lightness  might  be  supposed  to  absorb  and  con- 
dense considerable  quantities  of  vapour,  I  have  used  glass,  mica, 
and  various  metals ;  and  with  a  proper  amount  of  exhaustion 
they  all  act  in  the  same  manner.  The  fact  that  the  neutral 
point  for  platinum  is  close  upon  a  vacuum,  whilst  that  for  pith 
is  so  much  lower,  tends  to  d&ow  that  the  repulsion  is  not  due  to 
any  recoil  caused  by  condensable  vapour  leaving  the  surface 
under  the  influence  of  heat.  Were  it  so,  it  would  certainly 
require  more  vapour  to  be  present  when  platinum  had  to  be 
driven  backwards  than  when  pith  had  to  be  moved ;  but  the 
contrary  obtains  in  all  cases.  The  rule  seems  to  be,  the  greater 
the  density  the  higher  the  neutral  point. 

I  have  worked  with  all  kinds  of  vacua ;  that  is  to  say,  I  have 
started  with  the  apparatus  filled  with  various  vapours  and  gases 
(air,  carbonic  acid,  water,  iodine,  hydrogen,  &c.) ;  and  at  the 

E roper  rarefaction  I  find  no  difference  in  the  results  which  can 
e  traced  to  the  residual  vapour.  A  hydrogen  vacuum  seems 
neither  more  nor  less  favourable  to  the  phenomena  than  does  a 
water  vacuum,  or  an  iodine  vacuum. 

If  moisture  be  present  to  begin  with,  I  find  it  necessary  to 
allow  the  vapour  to  be  absorbed  by  the  sulphuric  acid  of  the 
pump,  and  to  continue  the  exhaustion,  with  repeated  heating  of 
the  apparatus,  until  the  aqueous  vapour  is  removed.  Then  and 
then  only  do  I  get  the  best  results. 

When  pith  is  employed  as  the  index,  it  is  necessary  to  have  it 
thoroughly  dried  over  sulphuric  acid  before  using  it,  and  during 
the  exhaustion  to  keep  it  constantly  heated  to  a  little  below  its 
charring-point,  in  order  to  get  the  greatest  sensitiveness. 

Professor  Reynolds  says,  ''  In  order  that  these  results  might 
be  obtained,  it  was  necessary  that  the  vapour  should  be  free  from 
air.''  On  the  contrary,  I  find  the  results  take  place  with  the 
greatest  sharpness  and  rapidity  if  the  residual  gas  consists  of 
nothing  but  air  or  hydrogen. 


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Rqmkion  accompanying  Radiation.  93 

Professor  Ueynolds  further  says^ '' Mr.  Crookes  only  obtained 
his  results  when  his  vacuum  was  nearly  as  perfect  as  the 
Sprengel  pomp  would  make  it.  Up  to  this  point  he  had  nothing 
but  the  inverse  effects,  viz.  attraction  with  heat  and  repul- 
sion with  cold.''  In  the  abstract  of  my  paper  published  in  the 
Proceedings  of  the  Boval  Society,  I  describe  an  experiment  with 
a  pith-ball  apparatus  in  which  the  neutral  point  is  7  millims. 
(about  I  inch)  below  the  vacuum,  repulsion  by  heat  taking  place 
at  higher  exhaustions.  At  the  Royal  Society  SoirSe,  April  22, 
1874, 1  showed,  and  fully  described  in  print,  the  apparatus  now 
before  you,  consisting  of  a  pith  bar  suspended  by  a  cocoon  fibre 
in  a  glass  bulb,  from  which  the  air  is  exhausted  until  the  baro* 
metric  gauge  shows  a  depression  of  12  millims.  below  the  ba« 
rometer.  Neither  attraction  nor  repulsion  results  when  radiant 
light  or  heat  falls  on  the  pith.  Exhaustions  of  7  and  12  mil- 
lims. are  certainly  very  inferior  vacua  for  a  Sprengel  pump. 

As  a  matter  of  fact,  however,  I  have  obtained  repulsion  by 
radiation  at  far  higher  pressures  than  these.  The  true  effect  of 
radiation  appeal's  to  be  one  of  repulsion  at  any  pressure,  over« 
balanced  when  a  gas  is  present  by  some  cause — possibly  air- 
currents,  but  probably  not.  I  have  already  explained  that  the 
barometric  height  of  this  neutral  point  dividing  attraction  from 
repulsion  varies  with  the  density  of  the  substance  on  which  ra- 
diation falls,  on  the  relation  which  the  mass  bears  to  the  surface, 
and  on  the  intensity  of  radiation.  By  modifying  the  conditions 
it  is  not  difficult  to  get  repulsion  by  radiation  when  the  appa- 
ratus is  full  of  air  at  nearly  the  normal  pressure  of  the  atmo- 
sphere. 

Professor  Reynolds  again  says, ''  The  reason  why  Mr.  Crookes 
did  not  obtain  the  same  results  with  a  less  perfect  vacuum  was 
because  he  had  then  too  large  a  proportion  of  air,  or  non- con- 
densing gas,  mixed  with  the  vapour.''  On  this  I  may  remark 
that  the  writer,  before  he  explained  how  it  was  I  could  not  get 
certain  results,  should  have  made  sure  that  what  he  assumed  to 
be  the  case  was  reallv  so.  I  have  not  the  least  difficulty  in 
showing  repulsion  by  heat  in  imperfect  vacua  when  mixed  va- 
pours and  gases  are  present. 

In  ray  arguments  against  the  air- current  theory,  I  have  shown 
that  the  best  results  are  obtained  when  the  vacuum  is  so  nearly 
perfect  that  an  induction-spark  will  not  pass  through  it.  This 
IS  an  equally  good  argument  against  the  presence  of  a  conden- 
sable vapour  as  it  is  against  that  of  air. 

From  the  construction  of  my  Sprengel  pump  I  am  satisfied 
that  the  vapour  of  mercury  is  absent  from  the  apparatus. 

The  following  experiments  have  been  specially  tried  with  the 
object  of  testing  this  theory.     A  tolerably  thick  and  strong  bulb 


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94      On  Attraction  and  Repulsion  accompanying  Radiation. 

it  blown  at  the  end  of  a  piece  of  eombnttion-tabing ;  and  in  it 
ii  supported  a  bar  of  aluminium  at  the  end  of  a  long  platinum 
wire.  The  whole  ii  attached  to  the  Sprengel  purop,  and  ex- 
haottion  it  kept  going  on  for  about  two  dayt^  until  a  tpark  will 
not  past  through  the  raeuuro.  During  thit  time  the  bulb  and 
itt  oontentt  are  frequently  raised  to  an  incipient  red  heat.  At 
the  end  of  that  time  the  tube  is  sealed  off,  and  the  bar  of  alumi- 
nium is  found  to  behave  exactly  as  it  would  in  a  lest  perfectly 
exhausted  apparatut;  vis.  it  it  repelled  by  heat.  A  timilar 
experiment,  attended  with  timilar  retultt,  has  been  tried  with  a 
glass  index.  It  is  impossible  to  conceive  that  in  these  experi- 
ments sufficient  condensable  gat  was  present  to  produce  the 
effects  Professor  Reynolds  ascribes  to  it  After  the  repeated 
heatings  to  redness  at  the  highest  attainable  exhaustion  (the 
gauge  and  the  barometer  being  level  for  nearly  the  whole  of  the 
48  hours),  it  is  impossible  that  sufficient  vapour  or  gas  should 
condense  on  the  movable  index  to  be  instantly  driven  off,  by  the 
warmth  of  the  finger,  with  recoil  enough  to  drive  backwards  a 
heavy  piece  of  metal. 

M ^  own  impi*ession  is  that  the  repulsion  accompanying  radia- 
tion IS  directly  due  to  the  impact  of  the  waves  upon  the  surface 
of  the  moving  mast,  and  not  aecondarily  through  the  interven- 
tion of  air-currentt,  electricity,  or  evaporation  and  condentation. 
Whether  the  setherial  waves  actually  strike  the  substance  moved, 
or  whether  at  that  mysterious  boundary-surface  separating  solid 
from  gaseous  matter  there  are  intermediary  layers  of  condensed 
gas  which,  taking  up  the  blow,  pass  it  on  to  the  layer  beneath, 
are  problems  the  solution  of  which  must  be  left  to  further 
research. 

In  giving  what  I  conceive  to  be  reasonable  arguments  against 
the  three  theories  which  have  been  supposed  to  explain  these  re- 
pulsions, I  do  not  wish  to  insist  upon  any  theory  of  my  own  to 
take  their  place.  The  one  I  advance  is  to  my  mind  the  most 
reasonable,  and  as  such  is  useful  as  a  working  hypothesis,  if  the 
mind  must  have  a  theory  to  rest  upon.  Any  theory  will  account 
for  some  fticts ;  but  only  the  true  explanation  will  satisfy  all  the 
conditions  of  the  problem,  and  this  cannot  be  said  of  either  of 
the  theories  I  have  already  discussed. 

My  object  at  present  is  to  ascertain  facts,  varying  the  condi- 
tions of  each  experiment  so  as  to  find  out  what  are  ^e  necessary 
and  what  the  accidental  accompaniments  of  the  phenomena. 
By  working  steadily  in  this  manner,  letting  each  group  of  expe-* 
rinients  point  out  the  direction  for  the  next  group,  and  follow- 
ing up  as  closely  as  possible,  not  only  the  main  line  of  research, 
but  ako  the  little  bylanes  which  often  lead  to  the  most  valuable 
results,  after  a  tin  e  the  facts  will  group  themselves  together 


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Mr.  J.  O'Kiuealy  on  Fourier's  Theorem.  96 

and  tell  their  own  tale.  The  eonditiona  under  which  the  phe- 
nomena invariably  occur  will  give  the  laws ;  and  the  theory  will 
follow  without  much  difficulty!  To  use  the  eloquent  language 
of  Sir  Humphry  Davy,  ''When  I  consider  the  variety  of  theories 
which  may  be  formed  on  the  slender  foundation  oi  one  or  two 
facts,  I  am  convinced  that  it  is  the  business  of  the  true  philo- 
sopher to  avoid  them  all  together.  It  is  more  laborious  to  accu- 
mulate facts  than  to  reason  concerning  them  ;  but  one  good  ex- 
periment is  of  more  value  than  the  ingenuity  of  a  brain  like 
Newton's/' 


XIV.  Fourier's  Theorem. 
By  James  (yKiNEiLY,  Bengal  Civil  Service*. 

THE  proof  given  of  Fourier's  theorem  in  all  the  text-books  I 
know  of,  is  a  modified  form  of  that  first  given  by  Poisson. 
What  is  at  present  proposed  is  to  prove  it  by  an  analytical  pro- 
cess for  periodic  functions,  and  to  show  that  it  is  simply  the 
solution  of  an  exponential  differential  equation. 

l{f{x)  =/[x+\),  where  X  is  the  wave-length,  we  have,  putting 
it  into  the  symbolical  form, 

or 

(6^*-l)/(^)=:0. 

It  is  a  well-known  theorem  in  differential  equations^  that  if  we 
get  an  equation  of  the  form  F(Djr)/(a')  =0,  and  can  find  the 
roots  of  F  (D,)=0,  the  equation  can  be  put  in  the  form 

(D,-«)(D.-«,)  (D.-«.).../(*)=0, 

where  a,  a^  a^  &c.  are  the  roots  of  F(D;r)»0,  and  that  the 
solution  will  be 

yt^)  =  Ae*" + A  ,€«»'+ AgC-** .... , 

A,  A„  Ag,  &c.  being  constants  depending  on  the  nature  o{/{x). 
In  the  present  case  F(Da.)  is  6^^*— 1.     Assume  D^asjsr,  and 
the  equation  to  solve  is 

or 
or 

or 


*  Communicated  by  tbe  Author. 

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96  Mr.  J.  O'Kinealy  on  Fouiier^s  Theorem^ 

(where  t  is  cipher  or  a  positive  integer),  or 

The  original  differential  equation  becomes  thus 

D,.(D.+  ?^X"'-  K=^)-/(*)=0, 
or 

^i  \      k  .  k        27ra?  ,  .         Afirx  , 

/(a?)  :=A  + A,  COS-r— +  AgCOS -r— +  .  •  .  . 

+  D,8in-:r h  B^  Sm  -rr-  .... 

At  At 

=A+SA,cos^ 
1=1  X 

+  2B,8in^^. 

*=l  A, 


This  is  Fourier's  theorem ;  and,  determining  the  constants  in 
the  usual  way  by  integrating  between  0  and  \,  and  by  multi- 

plying  by  cos  — .r—  .  sin  — —  and  then  integrating,  we  get  the 

A.  At 

usual  form, 

/W  =  s:  1  yi^)-^«+r2co8-^-— I  f{x)  coH-.r— dn 
A- Jo  ^'=»         ^   ^'o  ^ 


2'=«  .    2'irix 
+  -  S  sin  -^ 

A|  — I  A» 


j  /(^)8in-^-< 


In  the  same  way  we  can  obtain  other  forms  of  Fourier's  theo- 
rem. K  f{^)=Jlx  +  h),  we  have  generally  f{x)=f{x-{-nh), 
where  n  is  an  integer;  or  (c"*^— l)yi[a:)=0,  which  gives  the 
same  solution  as  above  if  we  put  nX  in  place  of  X. 

Hence  we  find 

iv  \      1  r%  \j    .    2  r*^-,  ,,  2to   V       Zirix  ^ 

^^^^X  ^^""^     '^^Jo  /(^)^«-^^^-nX--^^^^-7iX-^^- 

=  ^J^  /Wrfn+^^Scos--.J^  /(^).cos— rfn 

,    2  %«  .   27r?>   T"^^  ,     .   27r/ar , 

The  above  method  of  solution  may  be  applied  to  other  some- 
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Oa  the  Comtant  Currents  in  the  Air  and  in  the  Sea.       97 
what  similar  forms.     Suppose 

yi:;s+\)+/(x)=o, 

or 

The  roots  of  the  equation  e^^*  +•  1 =0  are 

where  t  is  any  odd  integer.     Hence 

f{x)  =  2  A|C08-r- 

+  S  B|  sin-r— J 

where  t  is  an  odd  integer. 

Several  other  theorems  of  a  similar  nature  will  readily  sug- 
gest themselves  as  capable  of  similar  treatment. 

11  Elysium  Row,  Calcutta. 


XV.  T/ie  Constant  Currents  in  the  Air  and  in  the  Sea :  an  At- 
tempt to  refer  them  to  a  common  Cause.  JBy  Baron  N.  Scbil* 
LING,.  Captain  in  the  Imperial  Russian  Navy. 

[Continued  from  p.  38.] 

B.  BOTATION  OF  THE  EaRTU  ON  ITS  AxiS. 

IN  the  daily  motion  of  the  earth  on  its  axis^  every  point  of  the 
surface  describes  a  circle.  These  parallel  circles  become 
smaller  and  smaller  from  the  equator  to  the  pole.  Now,  as  all 
points  of  the  surface  describe  their  circles  in  one  and  the  same 
time  of  nearly  24  hours,  it  is  evident  that  as  the  poles  are  ap* 
proached  the  velocity  of  motion  of  the  points  diminishes,  and 
this  in  the  ratio  of  the  cosines  of  the  latitudes.  As  already  men- 
tioned in  discussing  Hadley^s  theory  of  the  trade-winds,  a  body 
approaching  the  equator,  continually  coming  into  circles  of 
greater  velocity,  will,  in  consequence  of  the  law  of  inertia,  have 
the  tendency  to  perform  its  revolution  more  slowly  than  these ; 
and  hence  the  direction  of  motion  of  that  body  will  undergo  a 
westerly  deflection.  Conversely,  a  body  moving  from  the  equator 
will  b^  continually  meeting  with  parallel  circles  of  less  and  less 
velocity,  and  hence  will  take  a  direction  swerving  eastwards. 
Since  the  commencement  of  the  18th  century  the  correctness  of 
this  law  has  been  admitted,  and  it  has  been  made  use  of  to  ex- 
plain the  direction  of  the  trade-winds  and  many  other  pheno- 
mena. The  Academician  von  Baer,  for  example,  ascribes  it  to 
Phil.  Mag.  S.  4.  Vol.  4S.  No.  316.  Aug.  1874.  H 


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98  Baron  N.  SclulliDg  an  the  ComtatU  Ctarenit 

this  deviation  arising  from  the  eartVs  rotation  thatj  in  the 
northern  hemisphere,  all  the  rivers  which  run  in  a  meridional 
direction  undermine  their  right  banks — ^through  which  these 
banks  are  the  high;  but  the  left  the  low  ones.  The  whirling 
motion  of  cyclones,  or  Buys-Ballot's  law,  and  the  deviation  of 
the  meridional  currents  of  the  ocean,  are  all  explained  by  the 
axial  rotation  of  the  earth. 

It  is  indubitable  that  the  direction  of  every  independent  mo- 
tion on  the  surface  of  the  earth  receives,  through  its  rotation,  a 
certain  tendency  to  deviation;   yet  it  seems  to  us   that  the 
amount  of  this  deviation  is  only  too  often  greatly  overrated.    It 
is  usually  assumed  that,  in  consequence  of  inertia,  air  and  water 
particles  can  retain  for  hours  the  velocity  of  the  paralleb  which 
they  have  long  left  behind.     In  reality,  however,  the  friction 
and  resistance  of  other  particles  will  more  speedily  overcome  the 
inertia  and  comnel  the  particles  in  motion  soon  to  take  up  the 
new  rotation-velocity  of  the  parallel  circles  which  they  enter. 
It  must  also  be  remembered  that  the  velocity  of  adjacent  paral- 
lels only  very  gradually  changes;  and  therefore,  with  a  slow 
motion  of  the  particles,  the  least  friction  will  be  sufficient  to 
overpower  the  difference  existing  between  neighbouring  parallels. 
The  true  proportion  between  the  friction  and  the  tendency  to 
conserve  the  earlier  rotation-velocity  is  very  difficult  to  determine 
;  iccurately ;  nevertheless  it  seems  clear  to  us  that  the  deviation 
thereby  occasioned  in  the  direction  of  motion  in  a  short  time 
laust  always  be  very  inconsiderable.   The  defenders  of  Hadley's 
theory  will  admit  this,  although  they  generally  believe  that,  by 
itself  slight,  the  deviation  can,  by  continual  repetition  of  the 
action,  accumulate  and  so  become  gradually  considerable.  They 
think,  namely,  that  a  current  of  air  or  sea,  originated  by  differ- 
ence of  temperature,  flowing  along  the  meridian,  would,  when  a 
little  deflected  by  the  earth's  rotation,  continue  to  flow  in  this 
new  direction,  and  so  on.     In  other  words,  it  is  generally  be- 
lieved that  the  angle  which  a  current  makes  with  the  meridian 
must  continually  increase  with  *the  duration  of  the  current ;  and 
some  go  so  far  as  to  see,  not  only  in  the  south-west  wind  of  the 
middle  latitudes  of  our  hemisphere,  but  even  in  the  north-west 
wind  of  the  same,  an  antipolar  current  diverted  from  its  direc- 
tion by  the  rotation  of  the  earth.     But  this  evidently  false  con* 
elusion  results  from  the  false  assumption  that  a  current  onoe 
deflected  would  continue  to  flow  in  the  new  direction.     It  ia 
forgotten  that  the  rotation  of  the  earth  cannot  effect  a  deviation 
of  the  direction  unless  a  motion  is  present.     If  the  motive  force 
ceased  to  act,  the  current  would  soon  cease  also,  being  over- 
powered by  friction  and  other  resistance.     It  cannot,  therefore, 
flow  further  in  the  deflected  direction,  but  will  always  again 


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in  Uie  Air  and  in  the  Sea.  99 

teek  to  proceed  in  the  direction  in  which  the  force  acts  that  pro- 
duces the  motion^  therefore  in  that  of  the  meridian*  Now^  ao« 
cording  to  the  eiiating  theory,  two  forces  are  constantly  acting 
both  upon  trade-winds  and  the  meridional  currents  of  the  ocean  t 
—-of  which  the  one,  the  impelling  force,  springs  from  the  differ- 
ence of  temperature  of  the  equatorial  and  polar  regions^  and 
hence  operates  only  in  the  meridian-direction ;  while  the  otheri 
the  rotating  force  of  the  earth,  acts  in  coDsequence  of  the  inertia 
of  the  particles,  and  always  in  the  direction  of  the  parallel  circle, 
therefore  at  right  angles  to  the  motive  force.  If,  then,  both 
forces  remained  constantly  unaltered,  the  direction  of  the  current 
would  also  remain  invariably  the  same;  that  is,  the  angle  which 
the  current  forms  with  the  meridian  would  neither  increase  nor 
diminish.  In  our  case  the  action  of  the  force  in  the  meridional 
direction  must  be  assumed  to  be  constantly  uniform ;  while  the 
lagging  behind,  or  the  advance,  called  forth  by  the  transition 
into  other  latitudes  is  more  considerable  in  the  higher  than  in  the 
lower  latitudes,  because  the  parallel  circles  diminish  only  very 
gradually  in  the  latter,  but  rapidly  in  the  former.  From  this 
it  follows  that  the  deviation  from  the  meridional  direction  would 
necessarily  be  greatest  in  the  high  latitudes,  and  vice  versd. 
Every  current,  of  air  or  sea,  springing  from  difference  of  tem- 
perature would  therefore,  when  flowing  toward  the  equator,  come 
constantly  nearer  to  the  direction  of  the  meridian ;  while  a  cur* 
rent  flowing  away  from  the  equator  must  be  continually  adding  « 
a  little  to  the  angle  which  it  forms  with  the  meridian.  Accord- 
ing to  Hadley's  theory,  the  trade-winds,  flowing  to  the  equator, 
should  therefore  be  continually  approximating  nearer  to  the 
direction  of  the  meridian;  instead  of  which  we  see  just  the  op- 
posite^— that  at  thehr  polar  limit  they  blow  from  the  north-east  or 
south-east,  according  to  the  hemisphere,  and  as  they  near  the 
equator  they  come  ever  nearer  to  comcidence  with  the  direction 
of  the  parallel  drcles. 

The  sea-currents  of  the  southern  hemisphere  also  demonstrate 
that  the  earth's  rotation  has  but  little,  if  any,  influence  on  the 
direction  of  currents.  The  warm  currents  (those  of  Brazil  and 
Mozambique^  lean  to  the  east  coasts  of  the  continents,  and  are 
directed  to  tne  south-west,  instead  of  deviating  eastwards ;  while 
the  cold  currents  (those  of  Peru  and  South  Guinea,  and  the 
general  current  of  the  entire  Antarctic  Ocean)  agree  in  directing 
their  course  to  the  north-east,  instead  of  flowing  south-west  as 
required  by  the  theory  of  the  deviation  of  direction  arising  from 
the  rotation  of  the  earth.  We  see  in  this  circumstance  a  proof 
that  the  influence  of  the  rotation  is  in  the  whole  very  little, 
although  the  direction  taken  by  the  currents  of  the  northern 
hemisphere  appears  to  correspond  entirely  with  that  theory: 

H2 


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100  BaroQ  N.  Schilling  on  the  Constant  Currents 

namely^  the  Oulf-stream  and  the  Kurosiwo  flow  north-east ;  and 
the  cold  currents  of  the  seas  of  Japan  and  Greenland  go  aonth- 
west,  just  as  the  earth's  rotation  demands.  But  since  the  cur- 
rents of  the  southern  hemisphere^  notwithstanding  the  ample 
space  open  to  them,  are  quite  unaffected  by  the  rotation  of  the 
earth,  we  cannot  but  see  that  the  direction  of  the  currents  in  the 
northern  hemisphere  must  be  referred  to  other  causes.  The 
bend  which  the  Gulf-stream  makes  again  to  the  north  by  Cape 
Hatteras,  after  a  considerable  inclination  to  the  east,  seems  also 
to  speak  in  favour  of  our  view. 

If  the  rotation  of  the  earth  deflects  the  direction  of  the  sea- 
currents  only  inconsiderably,  then  its  influence  on  the  direction 
of  the  rivers  can  also  only  be  very  slight ;  but  even  the  slightest 
friction  of  the  water  flowing  along  the  bank,  if  constantly  re- 
peated on  one  side  during  thousands  of  years,  must  at  length 
perceptibly  undermine  the  bank ;  and  hence  Von  Baer's  view 
may  in  this  respect  be  right,  notwithstanding  the  extreme 
slightness  of  the  deflection  of  the  current. 

On  the  rotation  of  cyclones  we  will  speak  subsequently. 

Besides  the  action,  above  considered,  upon  already  existing 
currents,  many  ascribe  to  the  earth's  rotation  the  power  to  be 
independently  the  motive  cause  of  a  current.  MUhry,  for  in- 
stance, seeks  the  force  which  impels  the  equatorial  stream  in  the 
centrifugal  force  of  the  earth.  But  this,  as  we  know,  acts 
always  in  the  direction  of  the  radius  of  the  different  parallel 
circles,  and  hence  cannot  possibly  either  accelerate  or  retard  the 
rotation-velocity  of  the  water  and  the  air.  Miihry  evidently 
adheres  to  Kepler's  explanation  of  the  origination  of  the  equa- 
torial current,  by  the  water  staying  behind  the  general  motion 
of  the  earth.  This,  however,  contradicts  all  the  laws  of  mecha- 
nics, and  is  therefore  quite  inadmissible.  The  water  and  the 
air  adhere  to  the  globe  by  the  pressure  of  their  weight,  and 
must,  in  the  course  of  the  thousands  of  vears  during  which  the 
earth  has  turned  on  its  axis,  have  very  long  since  attained  the 
same  velocity,  through  friction,  since  velocity  once  acquired  is 
not  again  lost  so  long  as  there  is  no  resistance.  The  perma- 
nence of  the  earth's  rotation,  however,  sufficiently  proves  that 
in  the  universe  no  such  resistance  is  present.  The  phenomena, 
too,  of  both  air-  and  ocean-currents  absolutely  contradict  the 
assumption  that  the  water  and  air  are  subject  to  a  slower  rota- 
tion than  the  earth  itself. 

If  this  assumption  were  correct,  the  atmosphere,  being  less 
dense,  must  be  far  more  exposed  to  the  action  of  the  retardation 
than  the  water,  and  over  the  entire  surface  of  the  earth  wc 
should  constantly  have  strong  east  winds.  Besides,  although 
decreasing  from  the  equator  to  the  poles;  the  retardation  wo^d 


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in  the  Air  and  in  the  Sea.  101 

yet  be  perceptible  everywhere.  But  this  is  by  no  means  the 
case.  At  the  equator  itself^  or  in  its  vicinity^  no  such  current 
is  to  be  observed  either  in  the  air  or  in  the  water;  nay^  in  the 
equatorial  zone  we  find  that  the  sea  has  a  slight  current  flowing 
east ;  so  that  here,  not  only  is  no  retardation  to  be  traced,  but 
the  water  moves  faster  than  the  earth  turns.  In  the  zones  of 
the  Sargasso-seas,  again,  and  in  the  calms  of  the  tropics,  in  both 
hemispheres,  neither  in  air  nor  sea  can  any  diminution  of  the 
rotation-velocity  be  perceived.  Farther  polewards,  especially 
between  the  40th  and  50th  parallels  of  latitude,  the  constant 
west  winds  and  currents  flowing  east  testify  that  water  and  air 
move  eastwards  more  rapidly  than  the  earth  rotates.  This  cur« 
rent  in  the  atmosphere  in  the  middle  latitudes  is  explained  by 
the  anti-trades,  of  which  we  have  already  spoken.  It  expresses 
itself  in  the  sea  just  as  it  does  in  the  atmosphere ;  but  as  the 
anti-trade  explanation  is  absolutely  inapplicable  to  the  water> 
Miihry  accounts  for  the  sea-current  by  the  aspirating  force  of 
the  equatorial  stream.  Why,  however,  this  force  has  no  action 
at  all  upon  the  zones  of  the  Sargasso-seas,  but  goes  round  them 
in  a  wide  arc,  remains  unexplained.  Thus,  for  example,  in  the 
South  Atlantic  the  action  of  this  aspirating  force  stretches  along 
the  coast  as  far  as  the  Cape  of  Good  Hope,  and  thence  across 
the  ocean  to  the  American  shore.  If  the  aspirating  force  of  the 
Atlantic  equatorial  current  were  actually  so  great  that  its  influ- 
ence could  make  itself  perceptible  not  only  to  the  Cape  of  Good 
Hope,  but  also  from  there  to  the  American  coast,  then  it  could 
not  fail  to  lay  bold  of  the  Mozambique  current  at  the  Cape  and 
lead  it  into  the  Atlantic  to  supply  the  equatorial  stream.  Yet, 
as  is  well  known,  at  the  Cape  of  Good  Hope  the  Mozambique 
cunrent  makes  a  strikingly  sharp  bend  to  the  east,  and  returns 
on  a  wide  circuit  to  compensate  the  equatorial  stream  which 
flows  in  the  southern  part  of  the  Indian  Ocean,  after  first  wash* 
ing  the  west  coast  of  Australia.  The  insufficiency  of  the  expla- 
nation of  currents  by  aspiration  presents  itself  so  distinctly  that 
it  is  scarcely  necessary  to  dwell  longer  on  the  subject. 

The  earth's  rotation  cannot,  then,  generate  any  currents  in  air 
or  sea;  it  can  only  effect  a  slight  tendency  of  the  freely  moving 
air-  and  water-parcicles  to  shift  their  direction  towards  that  of 
the  equator.  This  tendency,  however,  is  so  feeble  that  from  it 
no  perceptible  current  can  arise;  hence  we  have  not  touched 
this  point  in  the  Russian  edition  of  this  work.  We  will  never- 
theless more  closely  consider  here  the  action  of  the  centrifugal 
force. 

Every  rotating  motion,  and  therefore  also  that  of  the  earth 
about  its  axis,  generates  a  centrifugal  force.  The  quantity  of 
this  force  for  every  single  point  of  the  earth's  surface  is  readily 


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102  Baron  N.  Schilling  on  the  Comiani  Currents 

jl^termined  by  dividing  the  tqnare  of  its  rotational  velocity  by 
the  radius  of  its  uarallel  circle.  It  thence  follows  that  the  oen* 
trifugal  force  of  the  earth  is  greatest  at  the  equator  (0*11124  foot 
in  a  second)^  and  from  that  to  the  poles  it  diminishes  in  the 
ratio  of  the  cosines  of  the  latitudes.  By  its  action  every  thing 
on  the  surface  of  the  earth  would  be  thrown  off,  if  the  earth's 
gravitation  were  not  greater  than  its  centrifugal  force.  Now 
kt  us  suppose  the  gravitation  of  the  earth  to  cease  to  act  during 
one  second.  Every  particle  not  firmly  adherent  to  the  earth 
would  instantly  leave  the  surface  and  continue  its  motion  in  the 
direction  of  the  tangent  of  the  corresponding  parallel  circle  with 
its  previous  rotational  velocity;  and  the  relative  distance  of  the 
particle  at  the  end  of  the  second,  from  its  point  of  separation, 
which  the  rotation  has  meanwhile  carried  forward  on  the  earth's 
surface,  would  serve  as  an  expression  of  the  quantity  of  the  cen<- 
trifugal  force  of  the  corresponding  parallel  circle. 

Thus,  if  a  particle  at  A  (fig.  1)  were  no  longer  subject  to  the 


Fig.  I. 


earth'sg^vitation,it  would 
oontinuo  its  motion  in  the 
direction  of  the  tangent 
AM,  and  after  the  lapse 
of  a  second  would  arrive 
at  M  instead  of  at  B.  A, 
the  point  at  which  it  was 
discharged,  would  mean- 
while  have  reached  B;  and 
B  M  would  denote  for  us 
the  centrifugal  force  cor- 
responding to  the  parallel 
circle  ABD.  Now  in 
reality  the  action  of  gravi* 
tation  never  ceases,  but  is 
constantly  directed  to  the  centre  of  the  earth,  therefore  at  a 
certain  angle  to  the  direction  of  the  centrifugal  force  B  M.  A 
freely  displaceable  particle  of  the  surface  would  thus,  under  the 
action  of  the  two  forees,  after  the  lapse  of  a  second  not  be  at  M, 
but  would  slide  on  the  surface  of  the  earth  to  F,  if  there  were 
no  friction  or  other  resistance.  Eveiy  particle  of  water  or  air, 
being  free  to  move,  must  thus  have  a  tendency  to  recede  from  a 
particle  (B)  firmly  adherent  to  the  earth,  and  to  approach  the 
equator  in  the  direction  of  the  meridian.  This  tendency  is  ex- 
pressed by  the  quantity  BF,  which  is  equal  to  BM.  sin  BMP, 
or  the  centrifugal  foree  of  the  parallel  cirele  multiplied  by  the 
sine  of  the  latitude.    The  centrifugal  force 

BMsiC.cos^, 


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m  the  Air  and  in  the  Sea.  108 

where  C  denotes  the  eentrifagal  force  of  the  equator,  and  ^  the 
latitade  of  the  parallel  circle.  Consequently  BF  n=  C  .  cos  ^ .  sin  (f>, 
and  therefore  reaches  its  maximum  quantity  when  ^=45^, 
•monnting  then  to  sin*45^x  0*11124  foot  3:0*05668  foot  in  a 
second^  or  4806*4  feet  in  24  hours  (which  makes  1^  verst, 
nearly  y  of  a  Oerman^  or  almost  exactly  ^  of  a  British  statute 
mile).  This  inconsiderable  tendency  toward  the  equator  is 
farther  diminished  by  friction,  and  therefore  cnnnot  possibly  be 
thought  of  as  the  inotive  force  of  a  current.  Yet  it  may  per- 
haps contribute  something  to  this — that  in  each  of  the  oceans 
the  current  flowing^  in  the  middle  latitudes^  from  west  to  east 
gradually  inclines  in  its  direction  a  little  to  the  equator.    . 

The  earth's  centrifugal  force,  acting  in  an  opposite  direction 
to  that  of  gravity,  occasions  over  the  entire  earth,  with  the 
single  exception  of  the  two  poles,  a  more  or  less  perceptible  di- 
minution of  weight.  This  is  greatest  at  the  equator,  amounting 
to  nearly  the  290th  part.  Thence  to  the  poles  the  quantity  to 
be  deducted  from  gravity  diminishes  in  the  ratio  of  the  squares 
of  the  cosines  of  the  latitudes.  Now,  as  all  bodies  (air  and  water 
not  excepted)  are  somewhat  lighter  in  the  vicinity  of  the  equator 
than  in  higher  latitudes,  one  would  think  that  this  must  pixnluce 
currents  in  the  ocean  and  atmosphere  equal  to  those  arising  from 
the  lightening  of  the  water  and  air  by  heating.  These  currents 
must  flow  beneath  to  the  equator,  and  as  upper  currents  from 
the  equator  to  the  poles.  But  in  reality  this  does  not  appear  to 
be  the  case;  for  degree-measurings  and  pendulum-observations 
have  shown  thai  the  surface  of  the  sea  has  the  form  of  an  ellip* 
toid  slightly  compressed  at  the  poles,  the  long  diameter  of  which 
(measured  in  the  plane  of  the  equator)  is  ^^^  of  its  length 
greater  than  the  shorter  diameter  (measured  in  the  line  of  the 
earth's  axis).  From  this  we  see  that  the  level  of  the  ocean  at 
the  equator  is  nearly  as  much  raised  as  the  weight  loses  there 
through  the  action  of  the  centrifugal  force;  hence  probably 
none,  or  a  scarcely  perceptible  portion  of  the  lighter  water  at 
the  equator  can  flow  off. 

It  is,  perhaps,  just  the  same  with  the  atmosphere;  yet  it  is 
probable  that,  with  diminished  pressure,  the  strong  elasticity  of 
the  air  will  produce  by  expansion  a  greater  raising  of  its  level 
(if  such  an  expression  can  be  used)  than  the  centrifugal  force 
requires.  If  it  is  so,  certainly  the  upper,  much  rarefied  air 
liiust  flow  off  from  the  equator,  and  be  replaced  by  an  under- 
current. Now,  since  the  mass  of  the  inflowing  and  of  the  out- 
flowing air  must  be  the  same,  the  dense  undercurrent  will  be 
considerably  less  perceptible  than  the  upper  strongly  rarefied 
one.  The  centiifugal  force  may  thus,  combined  with  the  differ- 
ence of  temperature^  generate  the  currents  in  the  upper  strata 


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104  Baron  N.  Schilling  on  the  Constant  Currents 

of  the  tropical  atmosphere^  and  bo  also  exert  a  certain  influence 
on  the  trade-winds^  bnt  cannot  possibly  develop  sufficient  force 
to  give  rise  to  those  winds. 

We  conclude  the  consideration  of  the  influence  of  the  eartVs 
rotation  on  air-  and  sea-currents  with  the  conviction  that  the 
existing  explanations  are  altogether  insufficient  for  the  currents 
which  flow  parallel  to  the  equator,  because  the  rotation  of  the 
earth  can  only  inconsiderably  alter  the  dii*ection  of  an  already 
existing  current,  whether  in  air  or  sea,  but  can  never  indepen- 
dently produce  a  current  of  any  importance. 

C.  Attraction  op  the  Sun  and  Moon. 

As  is  known,  all  the  heavenly  bodies  attract  each  other,  the 
force  therein  developed  being,  according  to  the  law  of  the  im- 
mortal Newton,  directly  as  the  mass  and  inversely  as  the  square 
of  the  distance  between  the  two  bodies.  If,  therefore,  we  take 
as  the  unit  of  mass  that  of  the  earth,  and  as  unit  of  distance  the 
semidiameter  of  the  earth,  then,  according  to  Newton's  law,  the 
force  with  which  the  sun  attracts  the  earth's  centre  will  be  ex- 

pressed  by     ■  g.     The  moon  attracts  the  centre  of  the  earth 

with  the  force  kph^f^q*'     The  ratio  of  the  attractive  force  of 

o\J[0\)y 

the  'other  heavenly  bodies  will  be  readily  found  in  the  same 

manner.  For  example,  the  force  with  which  Jupiter  attracts  the 
earth  when  nearest  to  it  is  one  25th  part  of  that  of  the  moon. 
The  action  of  all  the  rest  of  the  heavenly  bodies,  so  vastly  dis« 
tant,  is  again  considerably  less. 

Now,  as  the  force  with  which  a  given  heavenly  body  (the  sun 
for  instance)  attracts  the  earth  depends  entirely  upon  the  dis- 
tance between  the  two,  it  is  self-evident  that  the  parts  of  the 
earth's  surface  which  are  nearer  to  the  sun  must  be  exposed  to  a 
greater  attraction  than  those  more  distant.  This  can  have  no 
effect  on  the  solid  surface  of  the  earth ;  but  the  easily  displace- 
able  particles  of  the  sea  and  the  atmosphere  must  nave  their 
equilibrium  destroyed  by  its  influence;  and  to  restore  the  equi- 
librium currents  must  arise.  In  order  to  form  true  ideas  of 
these  currents,  it  is  absolutely  necessary  to  investigate  more  mi- 
nutely the  forces  which  call  them  forth,  and  the  action  of  these 
forces.     Before  all  things  we  must  realize  that  we  wish  to  con- 

*  We  have  assumed,  after  Klein  (Das  Sonnensystem),  that  the  mass  of 
the  sun  is  319500  times,  and  that  of  the  moon  one  80th  part  of  that  of  the 
earth.  For  the  mean  distance,  wc  have  assumed  that  tlie  distance  of  the 
sun  is  390  times  that  of  the  moon,  whot^mean  distance  we  estimate  at  60 
•emidiameters  of  the  earth. 


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in  the  Air  and  in  the  Sea. 


105 


gidcr^  not  tlie  absolute  motion  of  each  particle^  but  only  the  re- 
lative motion  of  the  particles  with  respeet  to  the  earth's  centre. 
Hence  we  have  not  to  do  with  the  whole  of  the  attraction  whibh 
any  heavenly  body  exerts  on  the  earth ;  the  difference  between 
the  forces  with  which  the  earth's  centre  and  the  point  of  its  sur- 
face to  be  considered  are  attracted  gives  the  limits  for  our  consi- 
deration. Thus^  e.ff.,  the  point  which  has  the  sun  or  the  moon  in 
the  zenith  is  nearer  to  this  heavenly  body  than  the  centre  of  the 
earth ;  and  the  difference  of  the  attraction  upon  these  two  points 

.  , , ,  ,  ,      819500        819500  -     ,,  , , 

might  be  expressed  by  -^g^^i  -  J234mj^  *""'        ^ 

80(59)*  "^  80(60)*  ^^^  ^^^  ""^°'  The  second  quantity  is  equal 
to  about  2^  times  the  first ;  and  from  this  we  infer  that  although 
the  attraction  of  the  sun  is  168  times  that  of  the  moon^  yet  the 
difference  between  the  attraction  of  a  point  at  the  surface  and 
the  centre  of  the  earth  by  the  moon  is  greater  than  the  same  by 
the  sun;  and  therefore  the  effect  produced  by  her  attraction 
upon  the  currents  of  air  and  sea  must  also  be  greater. 

For  all  other  heavenly  bodies  this  difference  is  so  slight  that 
we  need  not  take  it  into  consideration. 

Supposing  that  the  circle  ACED  (fig.  2)   represents  the 

Fig.  2. 


/ 

'^ 

"V 

/ 

K 

H 

P 

jw           ^      1 

\ 

/ 

/ 

earthy  L  the  place  of  the  centre  of  the  moon  or  sun^  and  that  k 
denotes  the  difference  between  the  attraction  of  a  point  at  the 
surface  and  the  centre  of  the  earth.  The  point  A  is  attracted 
more  strongly  than  the  centre  by  the  quantity  k^,  Now^  as  this 
attraction  in  the  half  of  the  earth  turned  towards  the  sun  or 
moon  acts  in  the  opposite  direction  to  the  earth's  attraction, 
^— it,  will  express  the  weight  of  any  particle  in  the  point  A,  the 
earth's  gravitation  being  denoted  byy.  At  the  point  B  the  dif- 
ference between  the  attraction  of  it  and  the  centre  will  be  some- 
what less.  Let  us  call  this,  difference  k^;  then  the  weight  at 
the  point  B  may  be  expressed  by  ^— Ar^.cosLBA;  for  here  the 


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106  Baron  N.  Sohilling  on  the  Constant  Currents 

attraction  of  the  moon  acts  at  the  an^le  LBA  with  the  earth's 
gravitation.  We  thus  see  that  the  weight  of  the  water  and  air 
becomes  greater  the  further  we  remove  from  the  point  where 
the  moon  or  the  sun  is  in  the  senith.  In  the  points  C  and  D, 
which  are  as  distant  as  the  centre  of  the  earthy  A=0;  therefore 
the  full  attraction  of  the  earth  corresponds  to  the  weight  of  the 
water  and  air  in  these  points.  In  the  other  hemisphere,  turned 
away  from  the  moon,  A  is  a  negative  quantity,  because  the  centre 
of  the  earth  is  more  powerfully  attracted  than  any  point  of  the 
surface  of  this  hemisphere.  But  k  acts  in  the  same  direction 
with  gravitation,  and  must  therefore  be  added  to  it  in  order  to 
determine  the  weight  of  a  particle  in  this  hemisphere.  The 
point  E,  most  remote  Arom  the  moon,  is  the  most  feebly  attracted ; 
hence  in  £  also  the  quantity  to  be  added  to  gravitation  is  the 
least,  and  the  weight  of  a  particle  in  E  lighter  than  in  any  of  the 
other  points  of  the  hemisphere  which  is  turned  away  from  the 
moon.  In  the  point  F,  tor  example,  the  weight  of  a  particle 
might  be  expressed  by^— A:3  •  cos  OFL ;  and  it  would  constantly 
diminish  the  more  we  approached  the  point  E,  which  has  the 
SUB  or  the  moon  in  the  nadir,  where  its  expression  would  be 
ff-^k^'  When  the  sun  is  in  question,  k^  is  only  slightly  less 
than  k^ ;  but  the  difference  is  not  insignificant  when  the  attrac- 
tion of  the  moon  is  taken  into  consideration ;  the  difference  be- 
tween the  attraction  of  the  point  which  has  the  moon  in  the 
zenith  and  that  of  the  centre  of  the  earth  is  1^  the  difference 
between  the  attractions  of  the  centre  and  the  point  which  has 
the  moon  in  the  nadir.  Briefly,  in  each  of  the  two  hemispheres 
(one  turned  to  the  sun  or  moon,  and  the  other  turned  from  it) 
the  minimum  of  the  weight  is  found  in  the  point  of  the  surface 
which  has  the  sun  or  moon  in  the  zenith  or  nadir,  but  the  maxi- 
mum on  the  line  D  M  G  N,  which  divides  the  two  hemispheres. 
The  pressure  of  the  greater  weight  must  cause  a  portion  of  the 
water  and  air  to  flow  into  the  region  where  water  and  air  arc 
lighter ;  and  hence  a  raising  of  the  level  will  take  place  there, 
corresponding  to  the  less  weight,  while  in  the  region  of  the 
greatest  weight  the  level  will  sink.  Consequently  both  the  sea 
and  the  atmosphere  must  endeavour  to  take  the  form  of  an  ellip* 
■oid  the  summits  of  which  are  on  the  line  which  passes  through 
the  centre  of  the  earth  and  the  moon.  By  the  action  of  the  suu, 
as  by  the  moon's  attraction,  an  ellipsoid  somewhat  less  elongated 
will  be  formed  in  the  sea  and  the  atmosphere,  its  major  axis 
being  on  the  line  which  passes  through  the  centre  of  the  earth 
and  the  sun.  In  reality  the  actions  of  these  two  attractions 
will  be  combined  and  form  only  one  tidal  ellipsoid,  which  is  most 
ekmgmted  when  the  actions  of  the  sun  and  moon  coincide--that 
is,  at  the  timet  9f  full  and  new  mp^Dr    On  the  contrary,  the 


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in  th  Air  and  in  the  Sea.  107 

ytising  of  the  level  will  be  less  when*  the  major  axes  of  the  two 
dlipaolda  are  perpendicular  to  each  other — that  ii^  at  the  timet 
of  the  first  and  last  quarters  of  the  moon. 

All  this  we  see  confirmed  in  nature  by  the  phenomena  of  ebb 
and  flow  of  the  tides.  Many  renowned  mathematicians  (among 
whom  Newton^  Euler^  Laplace^  and  Airy  occupy  the  first  place) 
have  endeavoured  to  determine  by  very  ingenious  mathematical 
calculations  the  laws  of  the  tides ;  their  theories^  however^  do  not 
in  all  respects  perfectly  agree  with  the  phenomena.  We  find, 
for  instance,  that  on  the  coasts  of  the  islands  in  mid*ocean  the 
tide  often  rises  only  a  few  inches^  and  seldom  amounts  to  more 
than  from  2  to  8  feet,  while  one  would  think  that  it  was  just  in 
the  open  ocean  that  the  tide  could  be  fully  developed.  Accord-* 
ing  to  the  theory,  the  tide  should  assume  the  greatest  dimen* 
sions  in  the  tropical  regions—instead  of  which,  we  find  that, 
with  very  trifling  exceptions,  it  is  very  moderate  in  the  tropics, 
and  does  not  reach,  by  a  long  way,  the  height  it  attains  in  the 
English  Channel  or  on  the  coasts  of  the  Bay  of  Fundy  in  Nova 
Scotia.  Airy  based  his  tide-theory  on  the  theory  of  waves,  and 
hence  ascribes  to  the  water-particles  only  a  vertical  oscillating 
motion.  But,  self*evidently,  there  cannot  be  anywhere  an  ele« 
vation  of  the  sea*face,  unless  the  necessary  water  flows  to  the 

Ci%  of  elevation,  water  being  incapable  of  elastic  expansion ; 
ce,  among  tidal  phenomena,  the  existence  of  a  horisontal 
motion  of  the  water  is  undeniable.  Nay,  the  horizontal  motion 
must  be  very  considerable,  since  it  is  dble,  in  the  course  of  a 
few  hours,  to  call  forth  a  not  unimportant  elevation  of  the 
water-surface  over  many  thousands  of  square  miles. 

If  the  earth  stood  still  and  the  same  points  had  the  sun  or 
the  moon  in  the  senith  constantly,  the  surface  of  the  sea  would 
probably  take  the  position  of  the  tidal  ellipsoid  given  by  the 
theory,  and  always  retain  the  same  form.  But  now  the  relative 
position  of  the  sun  and  moon  to  the  earth  is  perpetually  chang- 
ing through  the  rotation  of  the  latter ;  and  therefore  a  very 
large  volume  of  water  and  air  must  continually  flow  out  of  one 
part  of  the  ocean  into  the  other,  in  order  to  compensate  thefar^ 
extended  disturbance  of  equilibrium. 

Now,  as  the  relative  change  of  place  of  the  sun  and  the  moon 
i  s  very  rapid,  while  for  the  complete  formation  of  the  tidal  ellip* 
aoid  a  certain  time  is  necessary,  it  may  be  that  the  ellipsoid  has 
not  sufficient  time  to  take  its  perfect  form ;  the  tendency,  how- 
ever,  to  form  it  must  call  forth  currents  in  air  and  water,  which 
will  constantly  follow  the  motions  of  the  moon  and  the  sun.  If 
this  be  admitted,  it  explains  to  us  why,  in  the  open  ocean,  where 
these  currents  proceed  undisturbed,  no  tide,  or  a  very  slight  on^ 
is  observed  j  for  only  whe]:e  insufficient  depth  ox  the  shi^  of 


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108  Baron  N.  SchilliDg  on  the  Constant  Currents 

the  coast  detains  the  current  which  follows  the  sun  and  the 
moon  must  the  water  more  or  less  swell,  and  thereupon,  in  aa 
undulatory  motion,  push  the  swelling  further,  in  accordance  with 
the  law  of  the  wave-theory,  and  in  this  manner  carry  the  tide 
into  high  latitudes,  whither,  according  to  the  theory  of  the 
moon's  attraction,  it  should  not  come. 

We  are  confirmed  in  this  view  of  the  tides  by  the  circumstance 
that  the  tide*  wave  in  the  atmosphere  has  not  yet  been  observed, 
although  according  to  the  theory  it  must  show  itself  there  more 
considerable  than  in  the  sea.  The  question  of  the  atmospheric 
tide-wave  has  occupied  many  scientific  men.  Laplace,  after  a 
long  series  of  observations,  expressed  a  decided  opinion  that 
there  is  no  atmospheric  tide.  More  recently  Bouvard,  Eisenlohr, 
and  Sabine  have  thought  they  could  perceive  a  very  small  tide, 
expressing  itself  only  m  hundredth  parts  of  a  line  on  the  baro- 
meter-scale* 

By  the  way  we  must  remark  that  the  mercury  of  the  barome- 
ter, just  like  all  other  bodies  on  the  earth's  surface,  loses  a  por- 
tion of  its  weight  by  the  attraction  of  the  moon  and  sun ;  so 
that  it  cannot  show  the  variation  of  the  atmospheric  pressure 
produced  by  the  attraction  of  the  moon,  so  long  as  the  mass  of 
air  above  it  remains  the  same ;  every  current,  however,  must 
alter  the  height  of  the  mercury  column.  It  is  just  the  same 
with  respect  to  the  diminution  of  weight  effected  by  the  centri- 
fugal force.  An  aneroid,  as  such,  is  not  exposed  to  these  influ- 
ences, and  therefore  always  gives  the  absolute  pressure  of  the 
atmosphere ;  so  that  in  principle  it  is  preferable  to  the  barome- 
ter. In  practice,  however,  it  still  needs  considerable  improve- 
ments, because  errors  arise  from  the  metal  not  possessing  per- 
fect elasticity.  It  is  to  be  wished  that  observations  of  the  two 
instruments  were  more  frequently  compared. 

It  was  not  until  the  present  memoir  had  already  appeared  in 
Russian  that  I  got  a  sight  of  the  extremely  interesting  and  in- 
structive treatise  on  Tidal  Phenomena  by  Dr.  Schmick.  This 
writing  (which,  while  throwing  much  light  on  the  phenomena 
of  the  tides,  contends  for  many  views  to  which  we  cannot  assent) 
well  deserves  a  closer  consideration  than  would  be  in  place  here. 
Yet  we  cannot  omit  to  say  a  few  words  on  his  notion  of  the  dis- 
placement of  the  earth's  centre  of  gravity.  Since  the  height  of 
the  tide-wave  is  greater  in  the  hemisphere  turned  towards  the 
moon  or  sun  than  in  the  opposite  one,  Ur.  Schmick  thinks  that 
the  centre  of  gravity  of  the  earth  is  displaced  somewhat  towards 
the  side  of  the  greater  gathering  of  waters,  and  that  the  earth 
cannot  by  its  own  force  recover  its  original  centre  of  gravity 
after  it  has  suffered  displacement  from  without.  A  constantly 
repeated   displacement^  in  this  way,  of  the  centre  of  gravity 


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in  the  Air  and  in  tie  Sea.  109 

in  the  direction  of  the  southern  hemisphere  occasions  there^ 
according  to  Schmick^  an  accumulation  of  the  waters.  That 
the  centre  of  gravity,  displaced  by  external  force,  cannot  of 
its  own  accord  resume  its  former  position  is  perfectly  true; 
only  Dr.  Schmick  seems  to  have  forgotten  that  if  the  water 
rises  higher  on  the  hemisphere  turned  towards  the  moon  than 
on  the  opposite,  it  is  because  it  is  lighter  there  on  account  of  the 
greater  attraction  of  the  moon,  and  a  greater  gathering  of  the 
lighter  water  is  necessary  in  order  to  restore  equilibrium,  with* 
out  displacing  the  centre  of  gravity.  If,  therefore,  the  entire 
globe  consisted  of  a  liquid  and  had  no  rotation,  the  moon's  at- 
traction would  cause  it  to  take  the  form  of  an  ellipsoid,  of  which 
the  cusp  directed  to  the  moon  would  be  somewhat  higher  than 
the  cusp  turned  away  from  it;  but  the  centre  of  gravity  of  the 
entire  mass  would  remain  undisturbed  in  its  old  place,  because, 
as  already  said,  the  rise  of  the  water  on  each  point  must  be 
exactly  equivalent  to  its  loss  of  weight.  As,  however,  the  earth 
consists,  for  the  most  part,  of  a  solid  mass,  which  cannot  alter 
its  shape,  and  the  hemisphere  turned  to  the  sun  and  moon  loses 
more  of  its  weight  than  the  opposite  one,  the  centre  of  gravity 
must  be  displaced  in  the  opposite  direction  to  that  supposed  by 
Dr.  Schmick  ;  namely,  it  must  remove  to  a  somewhat  greater 
distance  from  those  bodies.  Of  course  the  displacement  is  only 
very  inconsiderable,  even  when  the  moon  is  at  its  least  distance 
from  the  earth ;  yet  it  may  to  some  extent  favour  temporary 
variations  of  the  atmospheric  pressure.  In  the  moon,  which 
constantly  shows  one  side  to  the  earth,  the  earth's  attraction 
must  thus  cause  the  centre  of  gravity  to  lie  permanently  on  the 
side  which  is  turned  away  from  us. 

When  the  tidal  wave  does  not  attain  its  greatest  height  at  the 
time  required  by  the  moon,  or  in  consequence  of  collateral  cir- 
cumstances attains  a  far  greater  height  than  the  moon's  at- 
traction demands  (as  in  the  Bay  of  Fundy,  the  English  Channel, 
and  many  other  places),  the  earth's  centre  of  gravity  will  cer- 
tainly remove  temporarily  in  the  direction  of  the  elevation  of  the 
waters;  but  Schmick's  view*,  that  the  water  must  spread  over 
the  surface  in  accordance  with  the  new  centre  of  gravity  as  soon  ' 
as  the  accumulating  force  ceases,  cannot  be  regarded  as  correct, 
because  any  excessive  accumulation  of  the  water  is. followed  by 
an  equal  sinking  of  the  level.  The  earth's  centre  of  gravity 
must  follow  these  oscillations  of  the  water,  and  hence,  when  this 
gradually  comes  to  rest,  will  probably  have  returned  to  its  old 
position. 

[To  be  oontinued.} 

•  Fluth^Phanmene,  p.  128. 


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[    110    ] 


XVI.  Apparatus  for  Measurement  ^L(nvPrei9ur^qfOai.  Bv 
TrofeuorWLzoD,  Indian  CivU'Engmeermg  CoUei,e,  Coopefs 
HillK 

THIS  apparatus  was  devised  for  estimating  the  pressure  of  a 
gas  when  its  tension  is  so  low  that  the  -^r--^^ 

indications  of  the  barometer  cannot  safely 
be  relied  on,  unless  indeed  a  very  wide 
barometer  and  an  accurate  cathetometer 
be  employed.  The  method  consists  in  con- 
densing a  known  volume  of  the  gas  into 
a  smaller  space  and  measuring  its  tension 
under  the  new  conditions. 

The  form  of  the  apparatus  is  the  follow- 
ing J — The  tube  a  communicates  with  the 
Sprcngel,  and  with  the  apparatus  to  be  ex- 
hausted ;  J  is  a  siphon-barometer  with  a 
tube  about  5  millimetres  in  diameter ;  and 
the  principal  parts  of  the  measuring-appa- 
ratus consist  of  c,  a  globe  of  about  48  cubic 
centims.  capacity  with  the  volume-tube  at 
the  top,  and  d  the  pressure-tube;  these 
two  are  exactly  of  the  same  diameter,  to 
avoid  error  from  capillarity.  The  tube  at 
the  bottom  of  the  globe  is  ground  into  a 
funnel-shaped  portion  at  the  top  of  the 
wide  tube  e ;  and  to  the  side  of  the  latter 
the  pressure-tube  d  is  joined.  The  volume- 
tube  at  the  top  of  the  globe  is  graduated 
in  millimetres  from  above  downwards,  the 
lowest  division  in  this  particular  apparatus 
being  45 ;  the  pressure-tube  d  is  also  gra- 
duated in  millimetres,  the  0  being  placed 
at  the  level  of  the  45th  division  on  the  vo- 
lume-tube. A  ball-and-socket  joint  con- 
nects the  bottom  of  e  with  a  vertical  tube 
/  about  800  millims.  long,  which  is  con- 
nected  at  its  lower  extremity  by  means  of 
a  flexible  tube  with  the  mercury-reservoir  g ; 
a  stopcock  at  h  permits  the  regulation  of 
the  flow  of  mercury  into  the  apparatus: 
this  may  be  conveniently  turned  by  a  rod, 
so  that  the  operator  may  watch  the  rise  of 

♦  Read  before  the  Physical  Society,  June  13,  1874. 
the  Society, 


Ccirirvnicated  by 


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On  an  Apparatus  far  Meaiurement  of  Low  Presiurei  of  Gas.  Ill 

tlu^  mereury  through  a  telescope  and  have  the  stopoook  at  the 
same  time  at  command, 

Ti'.e  volume-tube  was  calibrated  in  the  usual  way^  by  intro« 
ducing  weighed  quantities  of  mercury  into  it^  and  making  the 
necessary  corrections  for  the  meniscus.  The  capacity  of  the 
volums-tube,  the  globe^  and  upper  part  of  the  tube  e  was 
determined  by  inverting  the  apparatus  and  introducing  mercury 
through  e  until  the  mercury  flowed  down  the  pressure-tube  | 
the  weight  of  this  quantity  of  mercury,  divided  by  the  weight  of 
that  contained  in  tne  volume-tube^  gives  the  ratio  between  the 
volumes;  in  tlie  present  case  it  is  1  to  54*495.  While  the  appa^ 
ratus  is  being  exhausted^  the  reservoir  ff  is  lowered  so  as  to 
prevent  the  mercury  rising  out  of  the  tube  /;  but  when  it  is 
desired  to  make  a  measurement  of  the  pressure^  the  reservoir  is 
raised  and  the  mercury  allowed  to  pass  through  the  stopcock  h. 
On  the  mercury  rising  into  the  tube  e  it  cuts  off  the  communi- 
cation between  the  gas  in  the  globe  and  that  in  the  rest  of  the 
apparatus.  Ultimately  the  whole  of  the  gas  in  the  globe  is  con- 
densed into  the  volume-tube ;  and  its  tension  is  then  found  by 
measuring  the  difference  of  level  between  the  columns  of  mercury 
in  the  volume-  and  pressure-tubes.  On  dividing  this  difference 
by  the  ratio  between  the  capacities  of  the  globe  and  volume-tube, 
a  number  is  obtained  which  is  approximately  the  original  pres- 
sure of  the  gas;  this  number  must  now  be  added  to  the  differ- 
ence between  the  columns,  since  it  is  obvious  that  the  column 
in  the  pressure-tube  is  depressed  by  the  tension  of  the  gas  in 
the  remaining  part  of  the  apparatus ;  on  dividing  this  new  num- 
ber once  more  by  the  ratio  between  the  volumes  the  exact 
original  tension  is  found. 

An  example  will  best  illustrate  this.  A  quantity  of  gas  was 
compressed  into  the  volume-tube,  and  the  flow  of  mercury  was 
arrested  when  its  surface  reached  the  lowermost  division  on  the 
tube.     The  volume  was  then  ^.\  ^-=  of  its  original  volume,  and 

54*49  5  "     . 

the  difference  between  the  levels  of  the  mercury  m  the  volume- 
and  pressure-tubes  was  66*9  millims. ;  this  number,  divided  by 
54*495,  gives  1'228  as  the  approximate  pressure.  1*2  must 
therefore  be  added  to  the  observed  column,  which  thus  becomes 
68*1 ;  and  on  dividing  by  54*495,  the  number  1*2497  is  ob- 
tained as  the  actual  pressure. 

The  relations  existing  between  the  contents  of  the  other  divi- 
sions of  the  volume-tube  and  the  total  contents  of  the  gk)be 
were  determined  by  measuring  the  tensions  of  the  same  quantity 
of  gas  when  compressed  into  the  different  volumes.  By  this 
means  the  values  of  the  divisions  40,  85,  30,  25,  20,  15,  10,  9, 
8,  7,  6,  5,  4,  3,  and  2  have  been  found ;  the  experimenter  is 
thus  enabled  to  employ  a  division  suitable  to  the  quantity  of  gas 


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112  On  an  Apparatus  for  Measurement  of  Low  Pressures  of  Gas. 

with  which  he  has  to  deal.  The  Bmallest  division  contains  oq)/ 
149^2-35  ^^  ^^^  globe ;  consequently  when  a  quantity  of  gas 
hf^  been  condensed  into  this  space^  its  original  tension  wil!  be 
multiplied  1492*35  times.  In  one  case  an  amount  of  gas,  w'aich 
originally  filled  the  globe^  exhibited  a  pressure  of  onl^  *5  m'  llim. 
when  it  had  been  compressed  into  the  smallest  dinsion  c  f  the 
volume-tube ;  this  indicates  an  original  pressure  of  only  *00033 
millim. 

When  measuring  a  tension^  it  is  advisable  to  make  two  read- 
ings under  different  condensations,  and  to  take  the  mean  of  the 
results.  The  foUowbg  will  give  some  notion  of  the  precision 
attainable :— 

I.  At  division  5     -0225^      -kr^^  .noQn 
„        2    -0235/     Mean -0280. 


Mean  -0232. 


Bemeasured. 
At  division  5    -02281 
2    -0236/ 

II.  Barometer  0  millim. : — 

At  division  10     -igSSl       fuf  ^^  .moo 

5  -1980/      Mean  -1982. 

Remeasured. 

At  division  10     •1953\     t.,         ,^^^ 

6  -1967/     Mean  -1960. 

III.  Barometer  0*6  millim.  :— 

At  division  15     •5488*] 

„         10    -5488  y     Mean  -5492. 
„  6     •550lJ 

Remeasured. 
At  division  15     •54641 

„         10     -5464  y     Mcau    5469. 
„  6    •5480j 

IV.  Barometer  1  millim. : — 

At  division  20    1-20421      ^        .^^.^ 
„         15    1-2069/     ^^"  ^  '*"^^- 

Bemeasured. 
At  division  20    1-20821      ^i-        ,  ^^^ 
„        15    1-2099/     *'^^  1-2090. 

V.  Barometer  1*5  millim. :  — 

At  division  30    1-91391      t^        i.mAn 
„        25    1-9080/     Mean  1-9109. 

Bemeasured. 
At  division  30    190411      t.^        ,  ^^.^ 
„        25    1-9039/     M^^  ^'^^' 


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Dr.  W.  H.  Stone  on  Wind-pressure  in  the  Human  Lungs*    113 
VI.  Barometer  2*1  millims.: — 

AtdivisioaSS    2-60171      Mean  2-6045 
80   2-6078/     ^^^*^  ^  ^"^• 

Remeasured. 
At  division  35    261601      ^        o.., ^ 
30   2-6220  J     ^^"  ^  ^^^• 

It  may  be  mentioned  incidentally  that  connexions  for  appa<» 
ratus  may  be  conveniently  made  by  means  of  balKand-socket 
joints  of  glass.  The  ball  is  made  by  thickening  a  piece  of  tube 
in  the  bWpipe-flame^  and  the  socket  by  cutting  in  half  a  thick 
bulb  blown  on  a  glass  tube.  The  ball  is  then  ground  into  the 
socket  by  means  of  emery  and  solution  of  soda^  and  afterwards 
polished  with  rouge  and  soda  solution.  When  slightly  greased 
and  with  a  small  quantity  of  mercury  in  the  cup,  a  joint  is  ob<« 
tained  which  is  perfectly  air-tight  and  flexible*. 


XVII.    On  Wind-pressure  in  the  Human  Lungs  during  Perform^ 
once  on  Wind  Instruments.    By  Dr.  W,  H.  Stone f. 

THE  object  of  these  experiments  was  originally  physiological. 
It  had  been  stated  by  many  writers  that  the  forced  expi« 
ration  employed  in  playing  tended  to  produce  emphysema  of 
the  lungs ;  but  the  real  amount  of  such  pressure  had  never 
been  measured. 

The  facts  elicited  had  also  an  interest  of  a  purely  physical 
character,  which  was  the  principal  cause  of  their  being  brought 
before  this  Society,  although,  the  writer  of  the  paper  remarked, 
it  was  on  the  border-ground  between  two  great  subjects  of  study 
that  new  phenomena  were  often  to  be  looked  for. 

The  experiments  were  two  in  number.  The  first  aimed  simply 
at  measuring,  by  means  of  a  water-gauge,  the  extreme  pressure 
which  could  be  supported  by  the  muscles  of  the  lips,  both  in 
trained  musicians  and  in  persons  unaccustomed  to  the  con- 
tinuous exercise  of  these  organs.  The  difference  between  dif- 
ferent individuals  was  very  great,  some  untmined  persons 
having  naturally  considerable  muscular  power.  About  6  feet 
of  water  was  the  ordinary  maximum  when  a  small  tube  was 

*  Since  the  above  was  written  Dr.  Sprengel  has  pointed  out  that  Mr. 
Hartley  (Proc.  Roy.  See.  vol.  xx.  p.  141)  has  descnbed  as  a  ''Sprengel 
joint "  a  connexion  between  two  glass  tubes  made  by  grinding  a  conical 
tube  into  a  conical  cup  and  placing  mercury  or  water  in  the  cup.  The 
difference  between  this  and  the  one  above  mentioned  is  obvious:  the 
former  is  quite  rigid,  the  latter  perfectly  flexible. 

t  Read  before  the  Physical  Society,  April  18,  18/4.  Coiumunicated 
by  the  Society. 

PhU.  Mag.  S.  4.  Vol.  48.  No.  316.  Aug.  1874.  I 


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1 14    Dr.  W.  H.  Stone  on  Wind-pressure  in  the  Human  Lungs. 

inserted  between  the  lips.  When  the  lips  were  sapported  by  a 
cupped  mouthpiece,  such  as  is  used  for  brass  instruments,  a 
greater  height  of  the  column  could  be  obtained.  The  great 
majority  of  untrained  persons  could  not  support  more  than 
three  or  four  feet  of  water.  It  was  to  be  noticed  that  the  lip- 
muscles  invariably  gave  way  long  before  the  expiratory  power 
of  the  thoracic  muscles  was  exhausted.  By  pinching  the  lips 
round  the  orifice  of  the  tube  with  the  hand,  and  thus  prevent- 
ing their  yielding,  a  far  higher  column  of  water  could  be 
supported. 

The  second  experiment  consisted  in  introducing  a  small  bent 
glass  tube  into  the  angle  of  the  mouth,  connected  with  a  flexible 
tube  passing  over  the  shoulder.  It  was  found  that  most  instru- 
ments could  be  played  as  well  with  this  addition  as  without  it. 
It  obviously  established  a  communication  between  the  cavity  of 
the  performer's  mouth,  and  therefore  of  his  thorax,  and  the 
pressure-gauge.  The  following  Table  was  compiled  from  many 
observations  on  some  of  our  principal  English  musicians.  The 
person  experimented  on  was  placed  with  his  back  to  the  gauge, 
the  small  tube  was  inserted  in  his  mouth,  and  he  was  directed 
to  sound  in  succession  the  chief  notes  of  his  instrument.  As 
soon  as  the  tone  became  full  and  steady,  the  position  of  the 
water-gauge  was  noted.  A  fair  "  mezzo-forte "  note  was  em- 
ployed. Of  course,  by  forcing  the  wind  and  overblowing  the 
instrument,  much  greater  pressure  could  be  obtained;  but  those 
given  here  were  sufficient  to  produce  an  average  orchestral 
tone. 


Oboe     .     . 

•  lower  notes 

9  inches ; 

highest  17  i 

nch 

Clarinet      . 

•                  99 

15 

fy 

,1 

8 

„ 

Bassoon 

•                    9f 

12 

99 

f9 

24 

fi 

Horn     .     . 

if 

5 

Jl 

1> 

27 

99 

Comet  .    . 

}} 

10 

99 

99 

34 

99 

Trumpet     . 

•                    }f 

12 

99 

99 

88 

99 

Euphonium 

•               it 

3 

1> 

99 

40 

|> 

Bombardon 

•                     9} 

3 

99 

99 

86 

99 

It  is  to  be  noticed  that  the  clarinet,  in  this  as  in  some  other 
respects,  differs  from  its  kindred  instruments — and  also  that 
most  of  the  pressures  are  small,  not  exceeding  or,  indeed,  attain- 
ing the  pressure  of  a  fit  of  sneezing  or  of  coughing.  They  are 
therefore  very  unlikely  to  injure  the  lungs,  or  to  produce  the 
emphysema  erroneously  attributed  to  them. 


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C     115     ] 

XVIII.   On  the  Fall  in  PUch  of  Strained  Wires  through  which  a 
Galvanic' Current  is  pasting^    By  Dr.  W.  H.  Stone*. 

THE  object  of  this  paper  was  to  apply  tbe  vibrations  of  sound 
to  the  measurement  of  electrical  currents^.and  to  distin- 
guish what  was  due  to  heating-effects  from  those  caused  by 
alteration  of  elasticity. 

Strings  of  brass  and  steely  such  as  are  used  for  pianofortes 
(No.  16  gauge)^  were  stret^hed^  by  means  of  wrest-pins^  across 
a  resonant  box^  over  bridges  surmounted  by  brass  bearings^  and 
tuned  to  unison.  On  passing  a  current  fi*om  two  or  more 
Grovels  batteries  through  them,  a  very  marked  fall  in  pitch  wa? 
obtained.  The  vibrating  string  being  24  inches  long,  and  tuned 
to  two-foot  C,  the  tone  sank  above  a  fourth  in  steel  and  a  major 
third  in  brass. 

This  result  being  a  compound  of  actual  lengthening  by  heat 
and  of  other  causes,  it  was,  in  a  second  experiment,  endeavoured 
to  eliminate  the  former  element  by  straining  similar  strings 
between  the  same  bridged  by  means  of  a  weight.  This  was 
attached  to  the  arm  of  a  bent  lever,  to  the  short  end  of  which 
the  string  was  made  fast.  By  shifting  the  position  of  a  four^ 
pound  weight  along  the  arm,  very  accurate  unison,  or  definite 
periodicity  of  beats  could  be  obtained.  When  the  curi*ent  from 
the  battery  was  passed  through  this  string,  free  to  expand  by 
the  falling  of  the  weight,  and  therefore  at  a  constant  tension,  a 
fall  of  pitch  was  still  noticed.  There  was  also  a  very  marked 
loss  of  tone,  which,*  on  approaching  a  red  heat,  amounted  to 
total  extinction  of  sound. 

A  third  experiment  exhibited  the  changes  of  electrical  resis- 
tance in  a  wire  subjected  to  variations  of  strain.  The  wire  wlas 
accurately  balanced  against  another  resistance  in  a  Wbeatstone's 
bridge,  and  the  spot  of  light  from  a  mirror-galvanometer  join- 
ing the  two  circuits  thrown  on  the  screen.  On  suddenly  in- 
creasing the  tension  and  raising  the  musical  pitch  of  the  string, 
the  galvanometer  was  visibly  deflected.  This  was  not  an  effect 
of  heat  (since  the  balance  nad  been  brought  about  during  the 
passage  of  the  current),  and  must  be  due  to  altered  molecular 
state  caused  by  the  strain. 

It  was  incidentally  noticed  that,  when  beats  were  produced 
by  two  strings  on  the  same  sonometer,  they  continued  to  be 
sensible  to  the  touch  by  laying  the  hand  on  the  instrument  long 
after,  from  diminution  of  amplitude  in  the  vibration,  or  from 
slowness  in  the  beats  themselves,  they  had  ceased  to  be  audible,. 
This  afforded  a  good  demonstration  of  the  continuity  of  sensa- 
tion in  touch  and  hearing. 

*  Read  before  tbe  Physical  Society,  May  9,  18/4.  Communicated  by 
tbe  Society. 

12 

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[     116    ] 

X[£,  On  an  Improvement  in  the  Construction  of  the  Spectroscope. 
By  H.  G.  Madak. 

To  the  Editors  of  the  Philosophical  Magazine  and  Journal. 
Gentlbmen^ 

IN  the  '  Proceedings  of  the  Royal  Society/  No.  152,  p.  808, 
there  it  an  account  by  Mr.  Grabb  of  a  very  satisfactory 
method  of  correcting  the  curvature  of  the  spectrum-lines,  a  de« 
feet  inherent  in  all  spectroscopes  as  at  present  made.  This  dis-» 
tortion  is  due,  of  course,  to  the  fact  that  the  rays  from  different 
parts  of  the  slit  fall  on  the  prism  under  different  vertical  angles ; 
and  Mr.  Grubb  proposes  to  correct  it  by  making  the  slit  itself 
curved  instead  of  straight,  the  distorting  effect  of  the  prism 
being  then  simply  employed  in  rendering  straight  the  slit-images 
which  form  the  spectrum. 

I  think  it  just  worth  while  to  mention,  in  corroboration  of 
Mr.  Gkubb's  paper,  that  the  same  sufficiently  obvious  remedy 
oceurred  to  me  some  time  ago,  and  that  since  November  last  I 
have  had  curved  slits  in  use  for  a  lantern-spectroscope  with  per- 
fectly satisfactory  results.  These  are  screwed  on  (in  front  of) 
the  ordinary  slit-plates,  which  latter  are  opened  wide ;  and  the 
curved  plates  are  thus  readily  replaced  by  others  by  loosening  a 
couple  of  milled-head  screws.  Any  spectroscope  may  in  this 
way  have  the  additional  slit-plates  fitted  to  it  with  very  little 
difficulty  or  expense. 

I  have  two  pairs  of  slit-plates  with  curved  edges  thus  fitted  to 
my  original  slit : — one  with  edges  curved  to  a  radius  of  21  cen- 
tims.,  which  sensibly  corrects  the  distortion  of  a  single  carbon- 
disulphide  prism,  the  refracting  angle  of  which  is  60^ ;  the  other 
slit  has  a  radius  of  curvature  of  10  ccntims.,  and  is  used  with  a 
train  of  two  similar  prisms.  In  using  such  slits  with  a  conden- 
^ug-lens  between  them  and  the  prism,  they  should  be  so  placed 
that  the  centre  of  curvature  is  on  the  side  towards  which  the 
rays  are  refracted  by  the  prism.  The  above  curvatures  were  de- 
termined empirically  by  trials  with  tinfoil  slits,  which  were  easily 
made  by  attaching  a  piece  of  tinfoil  to  a  plate  of  glass  with  gum, 
and  (before  the  gum  was  dry)  cutting  out  very  narrow  strips  by 
a  knife  fixed  to  one  leg  of  a  pair  of  beam-compasses.  In  this 
way  a  number  of  trial  slits  may  be  made  and  tested ;  and  when 
the  curvature  of  that  one  which  performs  best  is  noted,  any 
good  optician  will  make  a  pair  of  brass  plates  with  edges  of  the 
proper  form. 

I  remain, 

Yours  faithfully, 

H.  G,  Madan. 

Eton  College.  July  18,  18/4. 


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[    117    ] 

XX.  On  the  General  Theory  of  Duplex  Telegraphy. 
By  Louis  Schwendler* 

Introduction. 
rpHE  name  of  "duplex  telegraphy '^  has  been  given  to  that 
-»-  node  of  electric  telegraphy  which  admits  of  the  simulta- 
neous transmission  in  opposite  directions  of  signals  between  two 
stations  through  a  single  wire.  That  this  name  is  far  from 
happily  chosen  is  evident ;  but  as  it  is  current  and  has  aJready 
gained  a  recognized  footing,  it  is  not  considered  advisable  to  en- 
deavour to  replace  it  now  by  a  more  rational  one,  and  it  will 
therefore  be  adhered  to  throughout  this  paperf. 

In  the  following  investigation  I  shall  endeavour  to  develop 
the  mathematical  theory  of  *'  duplex  telegraphy  *'  in  its  most 
general  form,  with  the  object  of  determining  not  only  the  best 
arrangement  for  any  particular  method,  but  also  the  relative 
values  of  different  methods. 

It  is  manifest  that,  having  from  general  considerations  decided 
on  the  best  method,  and  further  determined  the  best  arrange* 
roent  for  this  method,  the  remaining  diflSculties,  due  to  the 
nature  of  the  problem  itself,  will  be  exhibited  in  a  clearer  light, 
and  the  means  of  overcoming  them  may  then  be  more  easily 
discerned. 

It  is  believed,  however,  that  the  sequel  will  show  that,  if  the 
best  method  be  adopted,  and  for  this  method  the  best  arrange- 
ment be  selected  to  suit  the  particular  line  on  which  the  method 
is  to  be  employed,  the  difficulties  that  stand  in  the  way  of  duplex 
telegraphy  will  hardly  be  greater  than  those  which  are  encoun- 
tered every  day  in  ordinary  single  telegraphy. 

Imperfect  Historical  Sketch. 

Having  access  to  but  scanty  records  in  this  country,  I  am 
not  in  a  position  to  give  an  exhaustive'  history  of  this  most  im- 
portant invention ;  and  consequently  the  following  sketch  is  ne- 
cessarily incomplete,  and  must  be  taken  as  merely  introductory, 
it  being  relegated  to  those  better  situated  in  this  respect  than 
myself  to  clear  up  the  doubtful  points  of  priority,  and  produce, 
what  is  much  required,  a  complete  history. 

The  idea  of  sending  signals  in  opposite  directions  simulta* 
neously  through  a  single  wire  is  by  no  means  a  new  one.    As 

*  From  the  '  Jounial  of  the  Asiatic  Society  of  Beagm]/  vol.  xliii.  pt.  2, 
1874>  having  been  read  before  the  Society  on  the  4th  of  February,  1874. 
Communicated  by  the  Author. 

t  The  German  language  potsesses  a  peculiarly  suitable  word  in  "Oegert' 
sprecheH;'*  and  the  idea  is  fully  rendered  by  ** glekhzeitige$  Gegen-» 
sprtchen" 


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118  Mr.  L.  Schwendler  on  the  General  Theory 

early  as  1849  Messrs.  Siemens  and  Halskej  of  Berlin^  took  out  a 
patent  in  England^  for  the  simultaneous  transmission  of  a  plu- 
rality of  messages' by  a  suitable  combination  of  wires;  and 
although  this  patent  does  not  refer  directly  to  duplex  telegraphy 
as  it  was  subsequently  understood,  it  must^  notwithstanding^ 
be  regarded  as  a  forerunner  of  it.  In  point  of  fact.  Dr.  W. 
Siemens'!  idea  represents  the  general  problem  of  which  duplex 
telegraphy  is  only  a  particular  case. 

In  1854  Dr.  Gintl^  of  Vienna,  tried  his  ''compensation'^ 
method  of  "  duplex"  working  between  that  capital  and  Prague  fj 
and  on  the  30th  November  of  the  same  year  read  a  paper  before 
the  Kaiserlich-konigliche  Academic  of  Sciences  of  Vienna  ^  on 
the  practical  solution  of  the  same  problem  by  employing  a  Bain's 
electrochemical  telegraph-apparatus  instead  of  a  Morse's  receiv* 
ing  instrument. 

In  the  summer  of  1854,  after  Dr.  Gintl's  experiments  be- 
tween Vienna  and  Prague  had  brought  the  subject  prominently 
to  notice,  Messrs.  Siemens  and  Halske,  of  Berlin,  and  Herr 
Frischen  independently^  invented  the  "  differential "  method. 

In  January  1855  Edlund§  made  experiments  oh  the  line  be* 
tween  Stockholm  and  Gothenburg.  He  employed  a  ''differen* 
iial "  method,  which  he  had  invented  in  1848,  for  the  purpose 
of  measuring  accurately  Faraday's  *'  extra  currents." 

In  papers  read  at  Paris  on  the  I6th  July  and  6th  Aug^t, 
1855 II,  before  the  Academy  of  Sciences  by  M.  Zantedeschi,  he 
claims  the  honour  of  having  first  suggested  the  idea  of  duplex 
telegraphy ;  for  as  early  as  1829  he  had  proved  the  possibility 
of  the  simultaneous  transmission  of  currents  in  opposite  direc- 
tions through  a  single  conductor.  Having  never  seen  his  ori- 
ginal communication  of  1829,  it  is  impossible  for  me  to  say  how 
far  these  early  ideas  of  Zantedeschi  bear  on  the  problem ;  but  it 
is  certain  that  both  he  and  Dr.  Gintl  took  a  great  deal  of  trouble 
to  prove  an  erroneous  theory,  viz.  that  two  distinct  electrical 
currents  can  pass  simultaneously  in  opposite  directions  through 
the  same  conductor  without  in  any  way  interfering  with  each 
other.  Such  a  supposition  is  in  direct  opposition  to  the  elec- 
trical laws  which  were  already  known  in  18291,  and  besides 
is  in  no  way  required  in  order  to  explain  the  simple  pheno- 
nienon  of  duplex  telegraphy**. 

*  23rd  October,  1849.  The  actual  wording  of  the  English  patent  is 
unknown  to  me. 

t  Polyt.  Centralbl  1863,  p.  1476. 

X  Wien,  Akad,  Sittungsber,  zir. 

§  Pogg.  Ann.  1856,  vol.  xcviii.  p.  634.  H  Ibid.  p.  123. 

'  'If  Ohm  published  hisclatticfll  work  Die siakanische  Kette  mathemati$ck 
bearbeitet  in  the  year  1828. 

•♦  I>r.  W.  Siemens,  Pogg.  Ann,  vol.  xcviii.  p.  123, 


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qf  Duplex  TeUgrc^hy.  119 

*  None  of  the  above  methodd^  however,  came  to  have  ex- 
tended, or  indeed  any,  practical  application.  They  appear  to 
have  been  attempted  doabUngly  and  without  confidence;  and 
although  the  trials  are  generally  reported  to  have  been  bug- 
eeasful,  yet  the  methods  were  rejected  aa  impracticable,  and 
came  to  be  regarded  aa  merely  of  scientific  interest 'i'. 

Only  recently,  after  a  torpid  existence  of  almost  twenty 
Tears,  has  duplex  telegraphy  been  revived,  and  come  to  be  the 
leading  topic  in  telegraphy,  securing  after  such  a  lapse  of 
time  the  amount  of  public  interest  it  rightly  deserves. 

To  Mr.  Stearns,  an  American  telegraph-engineer,  is  due 
the  honour  of  having  appreciated  the  real  value  of  duplex  tele« 
graphy,  and  of  having  (by  giving  the  system,  modifiecl  by  im** 
provements  of  his  own,  an  extended  application  on  the  lines  of 
the  United  States)  proved  its  thorough  practicability. 

Inquiry  into  the  Caiues  which  have  delayed  the  introduction  of 
the  System. 

When  Steinheil  in  1837  announced  his  discovery  of  the  feasi- 
bility of  employing  the  earth  to  complete  the  electric  circuit  in- 
stead of  a  return-wire,  telegraph-engineers  immediately  recog- 
nised its  immense  mercantile  value,  and  did  not  delay  to  verify 
his  results. 

Now,  in  the  career  of  telegraphy,  the  invention  of  duplex  work- 
ing ranks  second  only  in  importance  to  SteinheiPs  discovery. 
The  utilization  of  the  earth  reduced  by  one  half  the  number  of 
wires  required  to  carry  a  given  traflSc :  duplex  telegraphy  again 
almost  halves  this  number.  In  the  face  of  this  fact  it  is  not  easy 
to  understand  why  the  one  idea  received  immediate  and  universal 
application,  while  the  other,  of  only  about  ten  years  more  recent 
date,  has  met,  until  now,  with  universal  neglect ;  but  on  closer 
examination  it  will  be  found  that  there  have  been  perfectly  com- 
prehensible, although  not  all  rational,  infiuences  at  work. 

An  inquiry  into  the  circumstances,  therefore,  that  have  caused 
ihe  discovery  of  a  system,  the  introduction  of  which  must  mark 
the  second  great  era  in  telegraphy,  to  lie  fallow  for  nearly  twenty 
years  is  of  the  utmost  interest,  and  cannot  fail  to  be  instructive 
with  regard  to  the  prospects  of  future  progress. 

From  an  examination  of  the  methods  originally  proposed  for 
duplex  working,  it  will  be  found  that  they  do  not  in  any  way 
essentially  dififer  from  those  which  may  now  come  into  actual 
use.  The  causes,  therefore,  which  have  prevented  the  intro- 
duction of  the  system  must  be  sought  for  external  to  the 
methods. 

.    *  For  the  light  in  which  daplex  tdegraphv  was  regarded  till  quite  lately, 
see  SchellcD,  Dab,  Sabine,  Blarier,  Kuho,  &c. 


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120  Mr.  L.  Schwendler  on  the  General  Theory 

The  fir&t  of  these^  we  find>  is  that  the  invention  was  in  ad- 
vance of  the  requirements  of  the  age.  Telegraph-lines  had 
already  been  constmcted  which  were  quite  capable  of  carrying 
the  given  traffic  and  even  more.  Further^  any  increase  in  traffic 
could  be  easily  met  by  an  increase  in  the  number  of  wires  on  the 
existing  telegraph-posts^  instead  of  by  resorting  to  a  system  which 
had  a  complex  appearance^  and  after  all  might  not  answer. 

However^  although  the  above  considerations  explain  the  course 
of  events  in  certain  limited  instances^  and  up  to  a  certain  time^ 
they  do  nothing  towards  justifying  the  costly  expedients  that 
have  been  generally  adopted  until  recently  in  preference  to  in- 
troducing duplex  telegraphy — for  instance,  the  reconstruction 
and  multiplying  of  long  overland  lines^  and  especially  the  laying 
of  a  second  submarine  cable  when  the  traffic  became  too  great 
for  one. 

•  It  is  time  that  the  successful  application  of  any  duplex  me^^ 
thod  requires  lines  of  a  more  constant  electrical  condition,  re- 
ceiving-instruments of  a  larger  range*,  and  telegraph-operators 
of  a  somewhat  better  professional  education  ;  but  surely  these 
three  conditions  have  not  all  at  once  become  fulfilled  (since  1872)| 
so  as  to  make  duplex  telegraphy  possible  only  just  now  f  No; 
the  causes  which  have  delayed  its  introduction  so  long  have 
been  of  a  much  less  technical  and  more  irrational  nature* 

The  mere  fact  of  the  duplex  methods  appearing  complex  pre- 
vented telegraph-administrations  from  thinking  seriously  of  in- 
troducing them.  The  ingenious  methods  were  never  tried  with 
that  zeal  and  perseverance  which  is  necessary  to  carry  a  new 
invention  successfully  through.  They  were  indiscriminately 
Injected  after  a  few  trials  made  without  method  or  considera- 
tion ;  and  the  real  conditions  of  success  or  failure  were  never 
examined  or  pointed  out.  Thus  naturally  a  prejudice  was 
created  against  duplex  telegraphy,  and  it  was  fostered  by  a 
host  of  school  literature  up  to  the  latest  time,  as  pointed  out 
before.  Further,  not  a  single  physicist  or  electrician  investi- 
gated the  question  with  a  view  to  ascertaining  what  quanti- 
tative effect  the  variable  condition  of  lines  has  on  duplex  work- 
ing as  compared  with  single  working. 

If  such  an  investigation  had  been  made,  it  would  have  been 
found  that  the  technical  obstructions  in  the  way  were  by  no 
means  so   formidable  as  had  been  represented,  and  that  the 

•  By  the  "  reuge  "  of  a  telegraph-instniment  I  undcrstnnd  the  ratio  of 
the  largest  to  the  smallest  force  by  which  the  instrument  in  question  can 
be  worked  without  requiring  a  fresh  mechanical  adjustment,  ror  instance, 
Siemens's  beautiful  relays  can  be  easily  adjusted  to  a  range  of  20 ;  i.  e. 
they  can  be  made  to  work  with  one  cell  through  an  external  resistance 
equal  to  their  own  resistance,  and  w  ith  ten  cells  tlirough  no  external  resist- 
ance, without  giving  the  tongue  a  fresh  adjustment. 


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ofDt^lex  Telegraphy.  121 

electrical  condition  of  the  lines^  as  well  as  the  perfection  of  the 
instraments  and  the  professional  education  of  the  staffs  would 
have  fully  admitted  of  the  successful  introduction  of  duplex 
telegraphy  at  least  ten^  if  not  twenty,  years  ago. 

It  is  true  indeed  that  the  suggestion  of  using  condensers  for 
balancing  the  charge  and  discharge  of  a  line  has  only  been  made 
very  lately,  being  one  of  Stearns's  happy  ideas ;  but  this  should 
have  been  no  reason  against  introducing  the  system  on  short 
and  overworked  lines,  where  the  charge  and  discharge  is  imper* 
ceptible.  If  only  one  telegraph -administration  had  shown  the 
perfect  practicability  of  the  system  on  a  short  line,  the  cloud 
of  prejudice  would  have  been  dissipated,  and  suggestions  for 
overcoming  the  charge  and  discharge  on  long  overland  lines 
and  submarine  cables  would  have  been  readily  enough  given, 
and  thereby  large  capitals  saved. 

To  sum  up,  therefore,  we  have  the  following  causes  which 
acted  persistently  against  the  introduction  of  duplex  telegraphy^ 

First,  the  invention  was  in  advance  of  the  age. 
.  Secondly,  the  telegraph  profession,  young  as  it  is,  is  far  more 
conservative  than  is  good  for  the  advance  of  telegraphy ;  and, 
on  the  whole,  telegraph-administrations  and  staffs  have  by  no 
means  that  professional  education  which  is  required  to  conduct 
practical  experiments  with  a  clear  understanding,  and  thence 
deduce  rational  conclusions.  Thus  prejudice  was  created,  which 
was  increased  from  year  to  year  by  authors  of  school  literature 
writing  most  discouragingly  on  the  subject. 

Thirdlv,  unfortunately  during  all  that  time  no  physicist  found 
it  worth  his  while  to  investigate  the  duplex  methods  with  a  view 
to  ascertain  quantitatively  what  can  be  expected  of  them,  and 
how  they  actually  compare,  with  respect  to  safety,  with  single 
working. 

Fourthly,  duplex  working  itself  could  not  progress,  because 
it  was  neither  tried  nor  investigated,  and  hence  no  sugges--! 
tions  for  overcoming  the  difficulty  of  charge  and  discharge 
were  called  for. 

Great  honour  must  therefore  be  given  to  Mr.  Stearns,  who 
brought  up  the  subject  again  so  prominently,  and  who  by  his 
zeal  succeeded  in  introducing  it  on  a  large  scale,  and  so  elevated 
the  ingenious  methods  from  the  questionable  position  of  '^  inter- 
esting scientific  exi>eriments.'' 

I  think  far  less  of  his  idea  of  introducing  condensers  or 
Ruhmkorff's  coils  to  balance  the  charge  and  discharge  of  lines> 
than  of  his  having  taken  the  neglected  child  up  again  against 
the  prejudice  of  his  own  profession,  and  shown  that  it  could 
have  a  healthy  existence  even  in  the  backwoods  of  Ameriea* 
I  trust  that  these  remarks  will  not  be  considered  irrelevant  in 


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I2i  Mr.  L.  Schwandler  on  the  General  Theoty 

the  present   iDvestigition,  siDce  they  tend  to  show  how  real 

Erogress  in  one  of  the  youngest  branches  of  applied  seienoe  may 
e  retarded  for  a  considerable  period  by  nothing  bat  prejudice 
of  the  profession  themselres^  for  whom  the  progress  should  be 
the  first  essential ;  and  administrations  will  see  how  much  the 
advance  of  telegraphy  will  always  depend  on  their  recognising 
and  encouraging  by  experiment  inventions  that  are  theoretically 
sound  and  tend  in  the  right  direction. 

General  Consideratiane. 

Before  entering  on  the  solution  of  the  problem  for  any  par- 
ticular duplex  method,  it  would  be  advisable  once  for  all  to 
state  definitely  the  nature  of  the  general  question  before  us. 
This  will  not  only  save  time,  but  the  subsequent  special  8olu« 
tions  can  then  also  be  made  under  a  general  guide ;  and  thus, 
being  well  linked  together,  the  whole  investigation  will  become 
£ir  more  lucid  and  concise  than  it  otherwise  would  be. 

While  in  ordinary  (single)  telegraphy  the  signals  are  always 
produced  in  the  same  way,  t.  e.  by  the  signalling  current  arri- 
ving through  the  line  from  the  distant  station,  the  signals  in 
duplex  telegraphy  may  be  produced  in  either  of  two  ways  essen- 
tially different  from  each  other.  Namely,  if  the  times  of  slid- 
ing from  the  two  stations  fall  together,  t.  e,  no  current,  or 
double  current,  or  any  difference  of  currents  is  in  the  line,  the 
signals,  so  long  as  this  state  of  the  line  exists,  are  produced 
wholly  or  partly  by  the  battery  of  the  receiving-station.  Sig- 
nals produced  m  this  way  we  shall  call  ^*  duplex  signals ;"  and 
these  signals  alone  indicate  the  essential  difference  between 
duplex  and  ordinary  telegraphy. 

If,  however,  the  moments  of  sending  from  the  two  stations 
do  not  fall  together,  the  signals  are  then  produced  as  in  ordi- 
nary telegraphy,  and  may  be  appropriately  designated  ^*  single 
signals.'^ 

It  will  be  clear,  then,  that  when  the  two  stations  are  at  work 
at  the  same  time,  "  duplex  signals  '*  and  "  single  signals  ^'  must 
necessarilv  follow  each  other  in  accidental  succession.  Nay, 
one  and  the  same  signal  produced  in  either  station  may  be  partly 
a  ^'duplex '^  and  partly  a  ''  single^'  signal. 

To  secure,  therefore,  regularity  of  working,  the  signals  pro- 
duced in  either  way  should  be  invariably  of  equal  strength. 

Further,  as  in  duplex  telegraphy  the  receiving-instruments 
must  be  always  permanently  connected  up  with  the  line,  it  is 
one  of  the  first  reauirements  that  the  out-going  or  sent  current 
from  any  station  snould  in  itself  have  no  effect  whatever  on  the 
reeeiving-instrument  of  that  station,  in  order  that  the  instru- 
ment may  be  entirely  fr^  \g  r^y^  ^gnals  from  the  disunt 


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of  Duplex  Telegraph}f.  123 

sUtioii,  Thus  we  invariably  have  two  conditions  to  fnlfil  in 
duplex  workings  independent  of  the  particular  method  adopted, 
namely  :i — . 

1.  The  reeewmg-ingtrument  of  each  station  ihouldnot  be  affected 
by  its  own  sending. 

2.  Tlie  duplex  signak  and  single  signals  must  be  of  equal 
strength. 

If  these  two  conditions,  which  are  necessary  and  sufficient, 
eould  be  always  fulfilled,  duplex  telegraphy  would  be  entirely 
on  a  par  with  single  telegraphy ;  for  the  sending  would  not  only 
not  interfere  with  the  receiving  (the  more  important  condition  of 
the  two),  but  the  received  signals  would  also  be  constant  in 
strength,  and  therefore  frequent  adjustment  of  the  receiving- 
instrument  would  be  no  more  required  than  in  single  telegraphy. 

Theoreticallv,  of  course,  every  duplex  method  hitherto  sue* 
gested  fulfils  these  two  conditions;  otherwise  the  method  would 
have  to  be  rejected  a  priori,  and  could  not  find  any  place  in  this 
paper. 

Practically,  however,  the  different  methods  may  behave  very 
differently  with  respect  to  the  fulfilment  of  these  two  conditions ; 
nay,  even  one  and  the  same  method  is  sure  to  give  quite  different 
results  in  this  respect  by  only  altering  the  magnitude  of  the 
resistances  of  which  the  arrangement  consists.  For  in  practice 
variations,  especially  in  virtue  of  the  line  having  by  no  means  a 
constant  electrical  condition,  are  necessarily  going  on.  These 
unavoidable  variations,  it  is  clear,  may  cause  very  diffei*ent  quan- 
titative disturbances  of  the  two  conditions  (1)  and  (2),  either  if 
we  compare  different  methods,  or  the  same  method  under  differ- 
ent resistance  arrangements. 

To  make  the  foregoing  clear,  we  will  designate : — 

by  p  the  force  which  acts  on  the  receiving-instrument  on 
account  of  not  being  able  to  fulfil  the  first  condition  absolutclv ; 

by  P  the  force  which  acts  on  the  same  instrument  when  the 
distant  station  is  sending  alone,  i.  e.  ^'  single  sisals;'' 

and  by  Q  the  force  which  acts  on  the  same  instrument  when 
both  stations  are  sending  simuUaneouslg,  i.  e.  **  duplex  signals.'^ 
.  Then  the  first  condition  (1)  is  expre^ed  by 

p-o, (I.) 

and  the  second  (2)  by 

P-Q«0. (II.) 

Further,  if  p  cannot  be  always  kept  rigidly  equal  to  zero  (on 
account  of  unavoidable  variations  in  the  system),  we  should  at 
leadt  have 

£-&sD  as  small  as  possible;     •    .    •    •     (III.) 


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124  Mr.  L.  Schweudler  on  the  General  Theory 

and  if  P  cannot  be  always  kept  rigidly  equal  to  Q,  we  should  at 
least  have 

P^QsbS  as  small  ^  possible^      •     .     .     (IV.) 

p,  V,  and  Q  being  functions  of  the  resistances  and  electromo- 
tive  forces  of  the  system^  which  are  known  so  soon  as  the  parti- 
cular duplex  method  has  been  selected. 

The  general  problem  which  is  to  be  solved  for  duplex  tele- 
graphy may  now  be  clearly  stated  as  follows  : — 

I)  and  S  are  two  known  Junctions  which  must  be  rigidly  equal 
to  zero  when  no  variation  in  the  system  occurs,  and  which  for  any 
given  variation  in  the  system  must  be  as  small  as  possible,  and  ap^ 
proximate  rapidly  towards  zero  as  the  variation  in  the  system 
becomes  smaller  and  smaller. 

Thus  the  solution  of  the  problem  for  any  civen  duplex  method 
will  always  be  a  question  of  the  minima  and  maxima  calculus. 

Having  then  ascertained  the  best  arrangement  for  each  duplex 
method^  the  methods  can  be  compared  inter  se;  and  that  method 
will  be  best^  and  should  be  selected  for  use^  which  for  any  given 
variation  in  the  system  gives  the  least  absolute  magnitude  to  the 
functions  D  and  S. 

If  we  suppose,  however,  that  the  particular  duplex  method  is 
not  given,  the  problem  to  be  solved  becomes  more  general,  but 
would  still  be  entirely  within  the  limits  of  the  variation  cal« 
cuius,  furnishing,  no  doubt,  a  very  interesting  and  important 
application  of  that  most  powerful  mathematical  instrument. 
The  general  solution  would  at  once  determine  the  best  method 
possible,  after  which  special  solutions  would  give  the  best  ar- 
i^ngemcnt  for  that  best  method. 

It  is,  however,  not  my  intention  to  endeavour  to  solve  here 
the  duplex  problem  in  this  most  general  form.  To  be  able  to 
indicate  so  general  and  desirable  a  solution  is  by  no  means 
identical  with  being  able  to  effect  it.  The  task  before  me  is  ht 
more  simple,  since,  as  already  pointed  out,  I  shall  investigate 
each  duplex  method  separately  to  determine  its  best  quantitative 
arrangement,  and  ultimately  compare  the  different  methods  to 
ascertain  their  relative  values. 

To  do  this,  the  question  may  be  attacked  in  two  different 
ways, .  depending  on .  the  purpose  for  which  the  solution  is 
required. 

Namely,  either  the  solution  is  to  be  made  when  considering 
the  line  as  a  variable  conductor  only,  but  not  acting  perceptibly 
as  a  Leyden  jar ;  or  the  line  is  to  be  considered  as  constant  in 
conduction  and  insulation,  but  acting  as  a  Leyden  jar  of  large 
capacity.  In  the  first  case  the  solution  would  be  directly  appli- 
tMt  to  short  overland  lines  (not  over  200  miles  in  length),  and 
in  the  second  case  to  submarine  cables,  which,  if  good,  may 


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of  Duplex  Telegraphy,  125 

always  be  considered  sensibly  constant  in  conduction  and  in- 
sulation. 

Further^  as  a  long  overland  line  acts  both  as  a  variable  con- 
ductor and  as  a  Leyden  jar  of  sufficiently  large  capacitv^  it  would 
then  be  necessary  to  give  a  solution  with  respect  to  both  these 
effects.  To  obtain^  however^  the  same  result  without  rendering 
the  problem  too  intricate,  it  will  be  best  to  separate  the  two 
questions  from  the  beginning,  and  afterwards  combine  their 
solutions  judiciously  for  application  to  the  case  of  overland 
lines. 

1st  Problem.  What  is  the  best  arrangement  of  any  given  duplex 
method  when  the  line  is  regarded  as  a  variable  conductor^  but  not 
as  acting  perceptibly  as  a  Leyden  jar? 

2nd  Paoblem.  What  is  the  best  arrangement  of  any  given  duplex 
method  when  the  line  is  regarded  as  a  Leyden  Jar  of  large  capacity, 
but  not  as  a  variable  conductor. 

The  second  problem  may  be  expressed  more  clearly  as  fol- 
lows:— 

2nd  Problem.  What  must  be  the  distribution  of  condensers 
along  a  given  resistance,  in  order  that  the  two  essential  conditions 
(I.  and  II.)  may  be  least  disturbed  for  a  speed  of  signalling  variable 
between  two  fixed  limits  ?  * 

*  A  tele|^raph-liDe  always  acts  as  a  condenser  with  capacity  and  con- 
duction-resistance in  each  point  of  its  entire  length,  while  an  artificial 
condenser  (such  as  a  Leyden  jar)  which  we  are  ahle  to  produce  sufficiently 
cheaply  has  only  capacity  but  no  perceptible  conduction-resistance  in  each 
point.  This  is  in  fact  the  essentud  difference  between  a  line  and  a  con- 
denser; and  therefore,  in  order  to  render  their  charges  and  discharges 
under  the  same  circumstances  as  nearly  as  possible  equal,  as  is  required 
for  duplex  working,  it  will  be  necessary  to  find  the  law  according  to  which 
to  distribute  a  certain  given  system  of  condensers  along  a  given  re- 
sistance. 

This  law  will  clearly  be  a  function  of  the  signalling  speed  within  its 
limits  of  variation.  For  instance,  say  the  signalling  sp^d  is  constant,  or 
its  range  zero,  then  clearly  one  condenser  connected  to  any  point  of  the 
given  resistance  would  suffice  ;  only  the  magnitude  of  the  capacity  of  this 
one  condenser  would  be  determined  bv  its  position  with  respect  to  the  re- 
sistance, and,  in  addition  to  this,  would  of  course  be  fixed  by  the  signalling 
speed  and  the  known  capacity  of  the  line. 

Further,  say  the  speed  of  signalling  is  variable  betwen  0  and  oo ,  or  its 
range  is  infinite,  then  clearly  only  an  infinite  number  of  small  condensers 
distributed  alon^  the  given  resistance  in  the  very  same  manner  as  the 
capacity  is  distributed  dong  the  line  would  strictly  answer  the  purpose  ; 
in  £ACt,  the  condenser  required  in  this  imaginary  case  would  be  nothing 
more  or  less  than  a  second  telegraph-line,  identical  with  the  one  used  for 
signalling.  In  practice,  however,  the  speed  of  signalling  varies  only  be- 
tween narrow  limits ;  and  therefore  the  number  of  condensers  required  to 
reproduce  as  nearly  as  possible  the  action  of  the  line  with  respect  to  charge 
and  discharge,  will  become  few,  especially  if  the  best  system  of  distribu- 
tion has  been  determined.     Until  this  law  is  known,  we  can  do  nothing 


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126  Mr.  L.  Schwendler  on  the  General  Theory 

It  U  clear  that  the  natare  of  these  two  problemg  ia  very 
different,  because  in  the  first  we  have  to  deal  with  forces  con- 
stant with  respect  to  time,  while  in  the  second  the  forces  acting 
are  functions  of  time,  i.  e.  of  the  signalling  speed.  (The  fwces 
in  this  case  are  proportioned  to  the  true  currents.)  The  latter 
problem  being  far  the  more  intricate,  and  for  my  special  purpose 
only  of  secondary  importance,  I  shall  begin  with  the  solution  of 
the  first. 

Solution  of  the  first  Problem  for  my  given  Duplex  Method, 

What  is  the  best  arrangement  of  any  given  duplex  method  when 
the  line  is  regarded  as  a  variable  conductor ^  but  not  as  acting  per'- 
ceptibly  as  a  Leydenjarf 

I.  The  bridge  method*. 

This  arrangement  for  duplex  working  is  based  on  the  well* 
known  method  of  comparing  electrical  resistances,  'MVheat-* 
stone^s  bridge ;''  and  the  figure  (p.  127)  gives  the  general  dia- 
gram when  this  method  is  applied  for  duplex  working. 

/9  is  the  internal  resistance  of  the  signalling. battery. 

1/  the  ^'measured  conductor ^^f  resistance  of  the  line  when 
measured  from  station  I. ; 


but  find  it  spproximately  by  experiment,  however  tedious  it  may  be  t« 
dose. 

It  has  also  been  proposed  to  use  Ruhmkorff's  coils  for  balancing  the 
effect  of  charge  ana  discharge.  This  method,  however,  I  l>elieve  must  be 
always  much  inferior  to  the  one  of  using  condensers,  inasmuch  as  the 
strength  of  a  voltaic  induction-current  scarcely  depends  on  the  speed  of 
signalling,  while  the  charge  and  discharge  of  a  line,  it  is  well  known,  is 
not  at  all  an  inconsiderable  function  of  the  signalling  speed. 

Therefore  if  the  strength  of  the  induction-current  had  been  a4insted  to 
balance  the  charge  and  discharge  of  the  line  for  a  certain  signalling  speed* 
the  balance  would  be  considerably  and  at  once  disturbed  if  tbs  speed 
varied  even  slightly;  and  since  so  long  as  hand  signalling  is  used  a  certain 
variation  in  the  speed  of  signalling  wiU  always  exist,  this  method  will  prove 
a  fisilure,  or  at  afi  events  will  render  fresh  adjustments  more  frequently 
necessary  than  when  condensers  are  used. 

*  Dr.  W.  Siemens  mentions  this  in  Pogg.  Ann,  vol.  xcviii.  p.  122  (1866). 

Mr.  O.  Heaviside  (Phil.  Mag.  1873,  voL  xlv.)  sUtes  that  Mr.  Eden,  of 
Edinburgh,  claims  to  have  suggested  this  method  at  about  the  same  time 
as  Mr.  Steams,  of  Boston,  U.b.A.,  took  out  a  patent  for  it. 

t  Genendly  these  measured  values  U  and  L"  will  be  different  from  each 
other,  especially  for  lon^  overland  lines.  They  can  become  equal  only 
under  two  conditions— either  if  the  resistance  of  the  resultant  fault  (t)  is  so 
great  that  the  total  conductor  resistance  of  the  line  (/'-|-r'as/}  can  be  nej^* 
lected  against  it,  or  for  any  magnitude  of  t  if  the  latter  has  a  position  m 

the  middle  of  the  conductor,  t.  e.  when  Ts/^a^* 


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of  Duplex  Telegraphy.  127 

JP  the  '' measured  conductor ''  resistance  of  the  line  when 
measured  from  station  II  i 

•••"=''+ i^- 

(f  the  complex  resistance  of  the  duplet  arrangement  in  station 
I.^  t.  e.  the  resistance  between  point  1  and  earth. 

fff  the  complex  resistance  of  the  duplex  arrangement  in  sta- 
tion 11.4 1.  e.  the  resistance  between  point  2  and  earth. 

£^  electromotive  force  of  the  signalling-battery. 

ffy  the  resistance  of  the  receiving-instrument. 


K,  telegraph-ke]^  of  peculiar  constniction^  to  be  described  hereafter. 

g,  the  receiving-instrument  eonnccted  up  in  that  branch  of  the  bridge 
which,  when  measuring  resistances,  would  contain  the  galvanometer*. 

a,  b,  and  d  are  the  branches  of  the  bridge. 

/,  the  resistance  between  the  rest-contact  of  the  key  and  earth. 

w,  an  additional  resistance  to  be  inserted  in  the  battery-branch,  for  rea- 
sons to  be  ^ven  further  on. 

t,  the  resistance  of  the  resultant  fault  {"  real  absolute  insulation  "  of  the 
line)  acting  at  a  distance  /'  from  station  I.  and  at  a  distance  f  from  sta- 
tion II.  (both  /'  and  T  expressed  in  resistances  so  that  f+r=sl  equal  the 
"  real  conductor  resistance  "  of  the  hue). 

To  be  quite  general^  we  must  suppose  that  the  telegraph-line 
which  connects  the  two  stations  I.  and  II.  has  a  different  resist- 
ance  when  measured  from  station  I.  than  when  measured  from 
station  11.^  and  that  therefore  the  best  resistance-arrangement 
of  station  I.  must  be  also  different  from  that  of  station  II.  with 
respect  to  magnitude  of  resistances. 

*  Siemens's  polarized  relays  are  well  adapted  for  this  purpose,  on  account 
of  their  great  sensitiveness  and  wide  range ;  D*  Arlincourt's  relays  would 
also  answer  well.  . 


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128  Mr.  L.  Schwcndler  on  the  General  Theory 

The  resistances  which  are  similarly  sitoated  in  both  the  sta- 
tions will  be  designated  by  the  same  letters ;  and  to  indicate  the 
station  to  which  they  belongs  each  letter  will  have  one  accent  in 
station  I.  and  two  accents  in  station  II. 

Further^  if  a  relatioa  between  the  resistances  of  one  station 
has  to  hold  good  between  those  of  the  other  station  also^  the  let- 
ters will  be  used  without  any  accents. 

The  great  practical  advantage  of  the  bridge  method,  it  will  be 
clear  at  once^  is  that  any  kind  of  receiving-instrument  which  has 
been  used  for  single  working  may  also  be  employed  for  duplex 
telegraphy.  This  fact  must  always  be  of  great  consideration  for 
any  administration  that  contemplates  the  general  introduction 
of  duplex  telegraphy. 

General  esfpressions  for  the  two  functiom  D  and  S. 

To  obtain  the  functions  D  and  S^  we  have  first  to  develop  the 
general  expressions  for  the  forces /»^  P,  and.Q>  say  for  station  I. 

By  j/  we  understand  the  force  which  acts  on  the  receiving* 
instrument  g^  of  station  I.  when  that  station  is  sending  alone 
(station  II.  at  rest). 

y,  in  our  particular  case,  is  therefore  proportional  to  the  cur- 
rent which  passes  through  the  galvanometer  in  a  Wheatstone^s 
bridge  when  balance  is  not  rigidly  established ;  thus 

where 

and 

N'=y(i'  +  dO(«'  +  c') +/{y(a' f  i'  +  c'  +  rf')  +  (^+rf')(«'  +  iO  } 

Further,  by  P'  is  understood  the  force  which  acts  on  the  re- 
ceiving-instrument in  station  I.  when  station  II.  is  SLnding 
alone :  single  signals. 

This  force  in  our  particular  case  is  proportional  to  the  current 
which  passes  through  the  receiving-instrument  of  station  I.  when 
station  II.  is  sending  alone ;  and  we  have  consequently 

where  C"  is  the  current  which  enters  the  line  at  point  2  when 
station  II.  alone  is  sending,  C"/jJ  the  part  of  this  current  C" 
which  arrives  actually  at  point  1  (on  account  of  leakage  between 
points  2  and  1,  a  part  of  C  is  lost),  and  CV'V^  ^hat  part  of  the 
current  C"/J  which  ultimatelv  produces  the  signal  {sirigle  signal) 
in  station  I.     The  current  CV'  arriving  at  point  1  branches  off 

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of  Duplex  Telei/raphtf.  129 

ia  two ;  one  part  goes  through  a*  and  the  other  through  ^  to 
earth. 
Farther,  n»_w »»" 


C»«E» 


w 


where 


FocE"^,m'i^; 


m!^ 


t 

and  N"  an  expression  identical  in  form  with  N'. 

Farther^  by  Ql  we  understand  the  force  which  acts  on  the 
receiying-instrument  of  station  I.  when  both  stations  are  send* 
ing  simoItaneoQsIy :  duplex  signals. 

This  force  is  again  proportional  to  the  current  which,  under 
these  circumstances,  passes  through  the  receiving- instrument  ^ 
of  station  I. 

This  current  can  be  expressed  by 

and  therefore 

a*  being  the  current  actually  in  the  line  at  point  I  when  both 
stations  are  sending  simultaneously ;  and  this  current,  being  the 
algebraical  sum  of  two  currents,  may  be  either  +,  0,  or  — . 
We  will  suppose  that  <r'  contains  the  sign  itself. 
Further,  we  have 

,     EW      E'W    , 

and  ^  is  a  function  which  becomes  identical  with  '^'  if  we  put 

Therefore  the  two  functions  D  and  S  are  for  the  bridge  me- 
thod (station  I.)  most  generally  expressed  as  follows : — 

E'N"    1    A'  ,„„. 

Phil.  May.  S.  4.  Vol.  48.  No.  316.  Aug.  1874.  K 

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ISO  Mr.  L.  Schwendler  on  the  General  Theory 

and 

s'^E'^/.y-^+o'^'j  .  .    (IV.) 

and  similar  expressioDs  will  be  obtained  for  station  II.,  namely 

and 

S''-F^M''^-^f+^^.     .    .    (IV".) 

Bigid  fulfilment  of  the  first  condition,  L  e.  D=0« 
For  statton  I.  we  have 

which  equation  can  only  be  satisfied  by 

since  the  other  factor  of  D'  cannot  become  sero  for  quantities 
larger  than  0  or  smaller  than  oo.  Then,  substituting  for  A'  its 
value^  we  have 

a'd'-4'(L'+/)=0; (V.) 

or  balance  in  station  I.^  when  that  station  is  sending  and  sta- 
tion II.  is  at  rest,  must  be  rigidly  established. 

Therefore  if  balance  in  station  I.  is  disturbed,  say  by  1/  vary- 
ing or  by  any  other  cause*  external  to  U,  we  most  have  means 
of  conveniently  reestablishing  balance  without  delay.  This,  of 
course,  could  always  be  done  by  altering  either  all  the  branches 
of,  V,  and  d!,  or  any  two  of  them,  or  only  one  of  them ;  but  it 
is  clear  that  so  long  as  the  variation  of  V  which  disturbs  the 
balance  does  not  exceed  certain  limits,  balance  may  be  regained 
by  altering  only  one  of  the  three  branches  available ;  and  as  this 
will  also  be  more  convenient  in  practice  than  altering  two  of  the 
branches,  or  all  three  simultaneously,  we  shall  make  the  suppo* 
sition  that 

"  Balance  is  reestablished  by  an  appropriate  readjustment  of  one 
of  the  three  available  branches"  f. 

*  Causes  of  disturbance  to  balance  external  to  L'  are  inappreciable  in 
practice  and  therefore  may  be  neglected  from  the  beginning. 

t  Finally,  when  the  hest  resistance-arrangement  has  been  found,  the 
resistance  of  the  different  branches  will  be  expressed  in  terms  of  L ;  and 
therefore  to  keep  the  best  arrangement  when  L  varies  between  any  two 
given  limits  will  involve  necessarily  a  simultaneous  alteration  of  the  resist- 
ance  of  all  the  branches. 

If,  however,  the  variation  of  L  is  small  in  eorapnrison  with  L  itself,  an 
alteration  of  one  branch  for  the  purpose  of  reestablishing  balance  is  justified, 
and  would  be  absolutely  correct  if  the  variation  of  L  \\erc  iufinitesimal. 


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of  Duplex  Telegrophy^  131 

The  question  therefore  is^  which  of  the  three  branches^  a,  b, 
or  d,  is  the  best  adapted  for  the  purpose? 

To  decide  this  we  must  remember  that  for  station  11.^  in  ac- 
cordance with  the  first  condition  (DsO)|  a  similar  equation  has 
to  be  fulfiHed,  namely^ 

fl"J"-J"(LW+p')«0.       ....     (V.) 

Now  o'^  the  complex  resistance  of  the  arrangement  in  station 
I.,  is  a  function  of  all  the  resistances  in  station  I. ;  and  similarly 
pf,  the  complex  resistance  of  the  arrangement  in  station  11.^  is 
a  function  of  all  the  resistances  in  station  II.  Therefore^  gene- 
rally, if  in  order  to  obtain  balance,  say  in  station  I.,  any  of  the 
three  branches  of,  V,  tP  were  adjustecC  ff  would  alter  in  conse- 
quence of  this  readjustment,  and  thereby  the  balance  in  station 
II.  (equation  Y".)  would  be  disturbed,  and  vice  ver$d.  In  other 
words,  the  readjusting  in  one  station  would  interfipre  with  the 
balance  in  the  other  station,  and  therefore  rigid  balance  could 
be  only  attained  after  a  series  of  successive  adjustments  in  both 
the  stations — and  then  only,  from  a  theoretical  point  of  view, 
approximately,  introducing  practical  difficulties  almost  insur- 
mountable. 

However,  examining  the  positions  of  the  three  branches,  it 
will  be  seen  at  once  that  b  acts  as  the  galvanometer-branch  of  a 
bridge  for  any  current  arriving  through  the  line.  Thus,  if  we 
were  to  fulfil  the  condition 

ad^fff^O (VI.) 

for  both  stations,  the  value  of  p  would  become  at  once  indepen- 
dent of  b^,  and  consequently  any  adjustment  of  V  to  reestablish 
balance  in  station  I.  would  not  affect  in  the  slightest  degree  the 
balance  in  station  II.,  and  vice  versd. 

Thus,  presupposing  the  fulfilment  of  this  condition  (equa- 
tion VI.)  for  both  the  stations,  the  branch  b  would  evidently  be 
the  best  suited  for  adiustmentf.  Under  these  circumstances  it 
would  then  be  clear  that  balance  in  either  station  can  be  obtained 
by  a  smgk  adjustment  of  b ;  and  therefore  we  mav  call  equation 
VI.  **  the  immediate-balance  condition  ;^'  and  the  fulfilment  of  this 
condition  being  of  the  greatest  practical  importance  to  ensure 
the  success  of  duplex  working,  we  are  justified,  nay  even  com- 


*   ^,(y+^)(«+/)_(arf~/y)« 


Therefore  if  ad—fg  is  very  near  sero»  p  becomes  most  rapidly  indepen- 
dent Of  b. 

t  Farther,  it  mutt  be  remarked  that,  even  if  the  condition  ad—fg^O  be 
not  rif^dly  fulfilled,  still  1^  adjusting  in  the  branch  b  we  have  '*  aecele* 
rated"  balance,  whereas  by  adjusting  in  a  or  d  we  should,  on  the  contrary, 
We  "retarded'*  balance. 

K2 


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132  Mr.  L.  Schwendler  on  the  General  Theory 

pelled,  to  use  this  relation  (equation  VI.)  as  the  basis  for  all 
subsequent  investigations. 

We  will  therefore  suppose  henceforth  that 

ad^fg^O (VI.) 

is  rigidly  fulfilled  for  both  the  stations. 

But  as  the  value  of  /  depends  on  the  position  of  the  key, 
which  during  signalling  moves  from  contact  3  to  contact  4  and 
back,  the  rigid  fulfilment  of  equation  (VI.)  necessitates  at  once 
that 

u;+i9=/, (VU.) 

not  only  for  both  the  contacts  3  and  4,  but  also  for  all  the  in- 
termediate positions  of  the  key.  Thus,  supposing  that  u^ + ^ »/> 
t.  e.  the  resistance  from  contact  4  through  battery  to  earth  equal 
to  the  resistance  from  contact  3  to  earth,  a  key  constructed  in 
such  a  way  that  contact  4  is  not  broken  before  contact  8  is  made, 
and  that  contact  8  is  not  broken  before  contact  4  is  made,  would 
fulfil  the  required  condition  entirely.  Keys  of  this  kind  can  be 
easily  enough  constructed.  It  is  true  that  in  any  such  key  there 
will  be  alwavs  a  moment  when  the  contacts  3  and  4  are  simul- 
taneous, and  when  therefore  the  resistance  to  earth  is  not  /,  as 

f 
it  ought  to  be,  but  only  ^.    Considering,  however,  that  the  time 

during  which  this  error  lasts  is  very  small  compared  with  the 
time  it  takes  to  make  a  signal,  its  disturbing  effect  will  never 
be  appreciable  in  practice ;  t.  e.  p  will  remain  sensibly  constant 
during  the  time  the  key  is  moved  to  produce  a  signal. 

There  will  be  no  practical  difficulties  connected  with  the  ful- 
filment of  equation  (VII.),  and  therefore  also  none  with  the  ful- 
filment of  equation  (VI.) ;  for  0,  the  internal  resistance  of  the 
signalling-battery  is  the  only  Quantity  which  of  itself  can  alter 
in  time.  However,  this  variation  of  fi  for  any  efficient  form  of 
signalling-battery  being  invariably  steady  and  small,  it  will  be 
always  possible  to  neutralize  its  action  in  time  by  a  simple  read- 
justment of  w. 

If  Leclanch^'s  cells  are  used,  or  well  prepared  Minotti's,  a 
weekly  adjustment  of  w  should  be  sufficient.  The  measuring 
of  ^8  will  always  be  an  easy  matter*. 

*  My  friend  Mr.  R.  S.  Brough  suggested  the  following  very  simple  me- 
thod for  keeping 

«^+/3=/. (VII.) 

Insert  a  small  galvanoscope  in  the  branch  b,  for  which  balance  is  estab- 
lished with  res|)ect  to  the  received  current,  t.  e. 

ad^fff^O (VI.) 

Now  note  the  deflection  on  the  galvanoscope  when  both  stations  are 


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of  Duplex  Telegraphy.  )  38 

Rigid  fulfilment  of  the  second  condition^  i,  e.  SsCX 
The  general  expression  for  S'  was 

S'=-j^Kr — ;f+^i>'^     •    •    •  (IV.) 
Bememberingthat  by  equation  (VII,) 

we  know  that  V^=<^;  and  substituting  further  for  a'  its  value, 
the  general  expression  for  S'  becomes 

S'--jprA*y— ^+  |-^--j^-^/|v^;  (m) 

and  this  form  of  S'  shows  at  once  that  it  is  perfectly  immaterial 
for  duplex  working  by  the  bridge  method  whether  the  same  or 
opposite  poles  of  the  two  signalling-batteries  be  put  to  line^;  for 
in  both  cases  equation  (IV.)  becomes 

S'=^V^-B'^ (IV.) 

Further,  it  will  be  seen  that  the  right-hand  member  of  eqna- 

A' 
tion  (I v.)  can  be  transformed f  into  E'm,  which  is  equal  to//, 

or  we  have  generally 

S^p; 

i.  e.  the  difference  offerees  by  which  duplex  and  single  signals  in 

sending  timultaneonslv,  snd  agsin  when  the  station  for  which  /3  is  to  be 
measured  is  sendinr  alone.  Then  dearlv,  if  these  two  deflections  are  equal, 
ID+/S  must  be  equal  to/.  If  the  two  deflections  are  not  eoualy  then  alter 
w  until  they  hecome  equal.  After  the  determination  is  maae  the  galvano- 
scope  is  short-circuited. 

*  In  practice,  however,  I  prefer  to  put  the  same  (namely  the  positive) 
poles  to  the  line,  as  then  defective  insulation  will  not  be  felt  so  much. 

t  We  have 

j^^mifc— All 


S= 


b      ' 

mAr—Afi 
EbA 


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184  Mr.  L.  Schwendler  on  the  General  Theory 

the  same  station  are  produced  is  equal  m  magnitude  and  sign  to 
the  force  by  which  balance  in  that  station  is  disturbed. 

Consequently  the  rigid  fulfilment  of  the  fint  condition  (DbO) 
will  entail  the  rigid  fulfilment  of  the  second  condition  (S=0) ; 
and  this,  it  will  be  clear,  is  only  due  to  the  fact  that  the  complex 
resistance  p  is  independent  of  b,  and  that  the  key  during  signal- 
ling does  not  alter  p ;  whence  it  follows  that  the  perfection  of 
the  key  in  this  respect  is  of  the  greatest  importance.  There  are, 
however,  no  practical  difficulties  connected  with  the  construction 
of  a  key  which  fulfils  condition  (VII.)  perfectly. 

By  the  aid  of  the  relations  giren  in  equations  (VI.)  and  (VII.) 
we  have  therefore  gained  the*great  practical  advantage  that  du- 
plex telegraphy  will  be  entirely  on  a  par  with  single  telegraphy, 
if  the  means  of  attaining  rigid  balance  are  sufficiently  accurate, 
eoavenient,  and  rapid. 

But,  even  sunposing  that  we  are  unable  to  keep  that  balance 
rigidly  for  any  length  of  time  (on  account  of  L  varying),  we  can 
nevertheless  bring  the  regularity  of  duplex  working  as  near  as 
possible  to  that  of  single  working  by  making  D  and  S  as  small 
as  possible. foe  any  given  variation  of  L« 

Rapid  approsimatian  of  the  twofunetions  D  and  S  towards  i$ro. 
For  station  I.  we  had 

s'=y«^^-^,    .  .  .  .    OV.) 

which  we  may  also  write 
since 


and 


Further,  if  we  call  V  the  value  of  b  which  in  station  L  esta- 
blishes rigid  balance  for  any  given  values  a',  d',  and  1/,  we  have 

A'=4'.SI/, 

where  SV  is  the  variation  of  L'  which  throws  the  balance  out, 
and  which  variation  may  be  either  positive,  eero,  or  negative 
(SL'  shall  contain  the  sign  in  itself). 


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of  Duplex  Telegrt^ky.  135 

Further,  substituting 


and 


•^'^ 


rt  ' 


the  expression  for  S'  may  be  written  as  foUovs : — 


8'»yocG 


1  , 


^-y 


zQ/¥', 


which  is  the  best  form  of  S'  for  our  purpose. 

The  function  S'  consists  of  two  factors — namelyi  of  C,  which 
at  or  near  balance  is  proportional  to  the  current  by  which  duplex 
and  single  signals  in  station  I.  are  produced,  and  of  V,  which 
at  balance  ssO. 

Therefore  to  make  S'  as  small  as  possible  when  balance  is 
disturbed,  we  can  only  do  so  by  making  F  as  small  as  possible, 

which  is  evidently  the  case  for  y's:  -^  a  maximum.    Further, 

S'-Q'F'; 
and  since  at  or  near  balance 

FaG', 
it  follows  that  j)/^  p . 

t.  e.  the  first  eondition  is  also  fulfilled  by 

y'ss  -^  a  maximum. 

Our  problem  for  station  I.  would  therefore  be  most  generally 
solved  if  we  make  the  function  ^  a  maximum,  remembering  that 
the  variables  contained  in  y'  have  to  fulfil  two  condition  equa- 
tions, namely  the  immediate  balance  (equation  YI.)  and  the  ba* 
lance  (equation  Y.). 

Substituting  for  m'  its  value,  and  remembering  that 

on  account  of  the  immeiiaie-balance  condition  (equation  IV.),  we 
get 


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136  Mr.  L.  Scbwendler  on  the  General  Theory 

But 

the  complex  resistance  of  station  I.  (the  expression  for  p  has  be« 
come  thus  simple  on  account  of  the  immediate-balance  condition 
VI.). 
Further, 

(on  account  of  balance  in  station  I.  being  established^  equationV.). 
Thus  we  have 

y'  =  p'  +  p"+I/ 

for  station  L ;  and  similarly 

for  station  II. 

Therefore  the  rapid  approximation  of  both  the  functions  D  and 
S  towards  zero  in  both  stations  is  obtained  \f  we  make  the  complex 
resistances  p!  and  p"  maxima. 

Now  the  form  of  p  shows  at  once  that  it  has  a  maximum  for 

•        (fl+/)=(y+rf), 
which,  in  consequence  of  equation  (VI.)>  gives  at  last 

«=^=rf=/. (VIII.) 

From  the  development  of  this  result  it  will  be  clear  that  the 
relation  expressed  by  equation  (VIII.)  must  hold  for  either. 
station  independent  of  L. 

All  that  now  remains  is  to  determine  b,  and  further  to  fix  the 
absolute  magnitude  of  any  one  of  the  branches.  Before  doing 
this,  however,  it  is  necessary  to  inquire  what  the  other  factor  of 
8,  namely  G,  becomes  in  consequence  of  fulfilling  the  regularity 
condition  as  expressed  by  equation  (VIII.). 

The  current  which  passes  through  the  receiving-instrument 
to  produce  ''single'*  as  well  as  "duplex''  signals  is  at  balance 
expressed  by 

^=^  •  7 — .    MT  / — .    N  .  o  / — rifv;  X  const., 
(a+y){L(a+y)+2%+rf)}  ' 

which  expression  has  a  maximum  for  either  a  or  g. 

The  maximum  of  G  with  respect  to  a,  it  will  be  seen,  contra- 
dicts the  regularity  condition,  since  a=^g^d  could  only  satisfy 

da 
if  d  were  negative,  a  physical  impossibility. 

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of  Duplex  Telegraphy.  187 

However^  the  maximum  of  G  with  respect  to  g  gives 

which  is  satisfied  by  a^g^d. 

This  is  a  fortunate  coincidence,  and  speaks  well  for  the  bridge 
method. 

Now  substituting  for  a  and  d  their  value  g  in  the  expression 
for  the  current  G,  we  get 

n      E      1 

and  this  expression  multiplied  by  ^g  gives  the  magnetic  effect 
of  the  receiving-instrument,  namely 

which  has  an  absolute  maximam  with  respect  to  g  for 

L 

Ftrrtfaer,  substituting  in  the  balance-equation  (V.) 
a  =  d=g=r^, 

^'-''  ft=| (IX.) 

Wc  have  therefore  the  following  two  equations  by  which  the 
problem  is  generally  solved : — 

a^g=d^f=\, (VIII.) 

*=i  =  B m 

by  L  being  understood  the  measured  conductor  resistance  of  the 
line  from  that  station  for  which  the  best  resistance -arrange- 
ment is  to  be  calculated. 

General  Results. 

1.  The  branches  of  the  bridge y  with  the  exception  of  the  one 
lying  opposite  the  line,  must  be  equal  to  each  other,  and  severally 
equal  to  half  the  measured  conductor  resistance  of  the  line. 

2.  The  branch  lying  opposite  the  line  should  be  equal  to  the 
sixth  part  of  the  measured  conductor  resistance  of  the  line;  and 
only  in  this,  the  smallest  of  all  the  branches,  should  readjustment  of 
balance  be  made. 

Nos.  1  and  2  necessitate  the  alteration  of  all  the  branches  if 
\i,  the  measured  conductor  resistance,  alters  within  wide  limits. 
A  determination  of  L  will  therefore  be  required  from  time  to  time. 


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188     On  the  Coloured  Wnge  of  Uniaccial  and  Biaxial  Crystals. 

From  the  development  of  these  general  retulti  it  frill  be  evi* 
dent  that  they  fulfil  the  following  conditions :— i» 

I.  7%6  irregtdarity  of  signals  in  the  one  station  is  entirely  inde^ 
pendent  of  the  irregularity  of  signals  in  the  other  station, 

U.  The  irregul^irity  of  signals  in  each  statitm  is  due  only  to 
balance  not  being  rigidly  established. 

III.  If  balance  in  either  station  is  disturbed,  a  single  adjustment 
in  the  branch  b  will  reestablish  that  balance. 

IV.  Any  disturbance  of  balance  will  have  the  least  possibh 
effect  on  the  received  signals. 

V.  Maximum  current  at  balance. 

VI.  Maximum  magnetic  effect  of  the  maximum  current  on  the 
receiving'instrument. 

[To  he  continued.] 


XXI.  On  a  simple  Arratwement  by  which  the  Coloured  Rings  of 
Uniaxial  and  Biaxial  Crystals  may  be  shown  in  a  common  Mi* 
croscope.    By  Dr.  W.  H.  Stonb*. 

THE  author  was  not  aware  that  any  arrangement  had  been 
hitherto  supplied  to  the  ordinary  microscope  other  than  an 
extra  top  to  the  eyepiece  containing  a  supplementary  stage  and 
an  analyzer.    This  could  only  be  considered  a  clumsy  expedient. 

The  objects  to  be  obtaineci  were  clearly  two : — ^first,  to  transmit 
the  ravs  at  considerable  obliquity  through  the'  plate  of  crystal ; 
secondlvj  to  gather  these  up  and  form  a  real  image  within  the 
tube  of  the  microscope.  Amici  had  accomplished  this  by  a 
special  combination  of  lenses  which  bears  his  name ;  it  might, 
however,  be  done  simply  by  placing  a  screwed  diaphragm 
on  the  end  of  the  upper  araw-tuoe  within  the  body  of  the  mi- 
croscope. The  screw  should  be  that  ordinarily  used  for  object- 
glasses.  To  this  an  object-glass  of  long  focus  was  fitted,  and 
another  of  higher  magnifying-power  in  the  usual  place.  The 
whole  body  was  then  drawn  out  and  adjusted  to  a  telescopic 
focus  on  a  distant  object.  The  lower  objective  formed  the 
object-glass  of  the  telescope,  and  the  inner  objective  with  the 
Huygenian  eyepiece  a  compound  ocular.  On  reinserting  the 
body  thus  arranged,  and  illuminating  the  crystal  on  the  stage 
with  convergent  light  by  means  of  a  condenser,  the  rings  and 
brushes  could  be  perfectly  seen.  The  whole  double  series  of 
rings  in  a  biaxial  crystal  of  carbonate  of  lead  was  thus  shown. 

The  condenser  used  was  a ''  kettle-drum  "  of  two  plano-convex 

lenses.    The  objective  on  the  nozzle  of  the  microscope  was  a  f 

of  Ross;  that  within  the  draw-tube  a  3-inch  objective  of  the 

same  maker. 

*  Read  before  the  Ph^-«ici4  Spn^t^i  June  13, 1874.    Comoniiucated  by 
the  Society. 


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[    189    ] 

XXII.  Modijhation  of  the  utual  Trombone  Apparaiuif^ 

the  Interference  of  8o9mi4>earmg  Wavet.  By  W.  r.  BabbbtTj 
F.I18.E.  hie.,  Profeeeor  of  Phyeia  in  the  Royal  College  of 
Science,  Dublin*. 

A  SIMPLE  apparatus  for  showing  the  interference  of  sound, 
bearing  waves  may  be  made  by  employing  a  circular 
arrangement  of  tubes,  one  sliding  within  the  other.  One  tube, 
A,  to  which  the  mouthpiece  M  is  fixed,  is  three  fourths  of  • 
circle ;  the  other  tube,  B,  to  which  the  n<»ile  N  is  attached,  is 
half  a  circle,  and  of  such  diameter  that  it  slides  freely  over  the 
tube  A. 

When  the  nossle  is  diame- 
trically opposite  the  mouth- 
piece, the  path  of  the  sound- 
waves is  of  equal  length,  and 
hence  the  sound  from  any 
convenient  source  placed  near 
to  or  within  the  mouthpiece 
is  distinctly  heard.  By  tum- 
ingthenozzletowardsN^nthe 
direction  shown  by  the  dotted 
lines,  one  limb  of  the  tube 
is  lengthened  whilst  the  other 
is  correspondingly  shortened; 
the  path  of  the  waves  being 
now  unequal,  a  point  is  soon 
reached  where  tne  sound  is  nearly  obliterated. 

Employing  a  suitable  source  of  sound,  and  a  sensitive  flame 
or  a  resonant  jar  as  a  phonoscope,  an  audience  can  perceive  at 
once  the  gradual  destruction  of  the  sonorous  pulses ;  and  more- 
over the  relative  lengths  of  the  two  branches  of  the  tube  clearly 
indicate  the  principle  of  interference  thus  illustrated. 

One  instrument  I  made  was  2  feet  in  diameter,  of  1-inch- 
square  zinc  tubing;  another  and  better  instrument  (skilfully 
made  by  Mr.  B.  H.  Bidout)  was  of  brass  tubing,  1  foot  in 
diameter,  the  one  limb  being  ^inch,  the  other  |^inch  tube. 
About  18  inches  in  diameter  would  probably  be  the  best  and 
most  convenient  size.  In  making  the  experiment,  care  should  be 
taken  to  avoid  {a)  the  conduction  of  sound  to  the  ear  by  the 
metal  substance  of  the  instrument;  (13)  the  direct  transmis- 
sion of  sound  through  the  surrounding  air.  The  latter  can  be 
overcome  by  attaching  a  sufficiently  long  gutta-percha  tube  to  M, 

*  Read  before  the  Physical  Society,  June  20, 1874.  Commuiiicated 
by  the  Sodety. 


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140  Notices  rejecting  New  Books. 

thus  removing  the  mouthpiece  to  a  diBtance  from  the  ear.  The 
former  can  be  obviated  to  some  extent  by  having  an  inelastic 
mouthpiece  or  similar  covering  to  the  end  of  the  tube.  But 
Mr.  Woodward's  device  of  putting  a  source  of  sound,  such  as  a 
reed,  entirely  within  the  tube,  and  a  trumpet  mouthpiece  at  N, 
is  undoubtedly  the  best  and  most  suitable  class  method  of  making 
the  experiment. 

.  F.S. — ^With  an  ordinary  pitch-pipe  inserted  at  N,  I  have  to-day 
(July  26)  repeated  the  experiment  to  the  class  of  science  teachers 
now  at  South  Kensington.  A  continuous  blast  of  air  was  driven 
through  the  pipe  from  an  acoustic  bellows ;  and  the  loud  note 
heard  at  first  was  utterly  extinguished  by  altering  the  relative 
lengths  of  the  tubes.  By  pushing  the  tube  still  further  round 
the  note  again  came  out;  thus  the  sound  of  the  pitch-pipe  could 
be  turned  on  and  off  at  pleasure.  Extinction  is  not  confined  to  a 
mere  line  in  adjusting  the  pipe,  but  spreads  over  a  short  and 
definite  range.  In  this  case  it  is  probaoly,  as  Professor  Ooodevc 
suggests,  the  interference  of  two  resonant  columns  of  air,  rather 
than  the  coalescence  of  two  progressive  waves  in  opposite  phases. 


XXIII.  Notices  respecting  New  Books. 

Statique  ExperimentaU  et  Theorique  des  Liquides  soumis  aux  seuUs 
Forces  MoUculaires,  Par  J,  Plateau.  2  vols.  8vo,  pp.  450  & 
495.  Ghent  and  Leipzig :  F.  Clemm.  London :  Trubner  &  Ca 
1873. 
T^HIS  work  consists  essentially  of  the  collected  series  of  papers 
-■-  "On  the  Figures  of  Equilibrium  of  a  liquid  Mass  without 
Weight,"  which  the  distinguished  physicist  of  Gthent  has  published 
in  the  *  Memoirs  of  the  Bel^n  Academy  of  Sciences  '  during  the 
years  1843  to  1868.  The  substance  of  these  papers  having  appeared 
Irom  time  to  time  in  the  pages  of  the  *  Philosophical  Magazme,'  in 
the  form  of  comparatively  full  abstracts  of  the  original  memoirs,  it 
is  not  needful  to  say  much  here  by  way  of  introducing  or  recom- 
mending the  work  to  our  readers.  It  should  be  observed,  however, 
that  this  book  is  not  merely  a  republication,  offering  simply  the 
convenience  of  presenting  in  a  collected  form  results  whicn  were 
previously  accessible  only  in  a  number  of  separate  papers  published 
at  intervals  during  a  period  of  twenty-five  years ;  thanks  to  the 
careful  revision  which  the  whole  has  received,  and  to  numerous  ad- 
ditions (some  of  them  of  considerable  extent,  relating  chiefly  to  the 
work*  of  other  investigators  in  the  same  field  of  research),  the  work 
before  us  possesses  much  of  the  continuity  and  completeness  of  a 
systematic  treatise. 

The  chief  scientific  interest  of  the  phenomena  which  Professor 
Plateau  has  investigated  lies  in  the  simplicity  of  the  physical  prin- 
ciple to  which  they  are  all  of  them  referrible,  and  in  the  compre- 


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Notices  respecting  New  Books*  141 

hensiveness  of  the  geometrical  relation  which  forms  the  mathematical 
expression  of  this  principle.  But,  independently  of  these  characters, 
which  are  inherent  in  the  nature  of  the  phenomena,  and  not  liable 
to  modification  in  consequence  of  the  greater  or  less  power  brought 
to  the  study  of  them,  the  present  book  derives  a  special  value  and 
beauty  from  the  sagacity  with  which  the  author  has  followed  out 
the  physical  and  mathematical  consequences  involved  in  the  prin- 
ciple of  the  equality  in  all  directions  of  the  tension  of  a  liquid  sur- 
face, and  in  the  resulting  geometrical  relation  of  the  constancy  of 
the  sum  of  the  principal  curvatures  of  such  a  surface,  comlnned 
with  the  completeness  and  accuracy  of  the  experimental  verification 
of  theoretical  deductions  which  he  has  obtained.  In  fact,  the  judg- 
ment and  ingenuity  shown  in  devising  the  methods  of  experiment, 
and  the  skill  with  which  they  have  beien  applied,  have  enabled  the 
author  to  trace  out,  with  a  minuteness  that  has  not  often  been 
equalled  in  other  branches  of  Physics,  the  characteristics  of  the  phe- 
nomena under  investigation.  These  phenomena  also  being  compa- 
ratively simple,  in  the  sense  of  its  being  possible  to  isolate  almost 
completely  by  the  methods  adopted  the  effects  of  the  particular 
causes  it  was  the  author  s  object  to  study,  these  researches  form  a 
remarkable  example  of  the  close  correspondence  between  theory 
and  experiment,  worthy  to  be  compared  with  Schwerd's  memo- 
rable work  on  the  Phenomena  of  Diffraction,  a  work  with  which 
Professor  Plateau's  presents  another  point  of  analogy  in  the  familiar, 
every-day  character  of  many  of  the  phenomena  with  which  it  deals. 

ContrihiUioTis  to  Selenography,  By  William  Eadclifp  Bibt, 
FJl^AJS,,  F.M.S.  London :  Taylor  and  Francis.  1 874. 
We  are  glad  to  see,  by  a  copy  of  the  above  work  which  we  have 
received  for  review,  that  Mr.  Birt  has  put  together  in  one  volume 
his  more  recent  labours  connected  with  Selenography ;  for  not  only 
are  there  to  be  found  among  them  able  discussions  of  matters  con- 
n3cted  very  closely  with  interesting  questions  of  present  interest  in 
t*ie  science,  but  we  are  convinced,  from  a  careful  examination  of 
Mr.  Birt's  production,  that  it  will  prove  of  great  value  to  every 
shident  of  the  lunar  surface  who  may  possess  a  copy — and  that 
not  only  because  in  future  years  it  will  be  a  work  to  which  the  ama- 
teur may  turn  to  compare  his  own  observations  with  those  there 
recorded  of  some  of  the  most  minute  of  all  lunar  objects,  in  the  full 
confidence  that  they  were  carefully  drawn  and  correctly  described 
for  the  epochs  of  observation,  but  because  it  is  a  volume  likely  to 
be  of  essential  service  to  every  real  student  in  connexion  with  his 
own  method  and  mode.  Headers  of  the  Eeports  of  the  British  As- 
sociation for  the  Advancement  of  Science  will  remember  that  in 
1864  the  Association  voted  a  grant  for  the  purpose  of  mapping  the 
surface  of  the  moon,  which  was  continued  for  three  years — the  re- 
sult being  that  three  areas  of  the  contemplated  map,  on  a  scale  of 
230  inches  to  the  moon's  diameter,  by  Mr.  Birt,  with  catalogues  <rf 
the  objects,  were  published  in  the  volumes  for  1866  and  1868.  The 
first  of  Mr.  Birt's  contributions  to  Selenography,  published  inde- 


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142  Notkes  respecting  New  Booh, 

pendentlj  of  the  Assodatioii  in  1870,  is  a  fourth  area  of  tiie  map* 
in  continuation  of  the  original jphm,  and  which  occupies  the  first 
pkce  in  the  present  Yolume.  Facing  page  1  we  have  an  excellent 
map  of  the  area,  carefully  drawn  in  outline,  accompanied  hy  a  full 
descriptive  Catalogue  oi  99  craters  and  other  objects  situated  upon 
the  area.  The  description  is  completed  by  a  comparison  of  four  pno- 
tograms*  The  numerous  notes  and  woodcuts  of  interesting  objects 
must  be  highly  suggestive  to  every  earnest  stud^it. 

The  very  complete  monograph  of  the  Mare  Serenitatis  is  of  itself 
a  work  capable  of  sustaining  the  reputation  of  the  author  of  the 
four  areas,  comprising  as  it  does  so  large  a  descriptive  catalogue  of 
objects  within  tnu)  la^e  and  perhaps  b^t*known  of  all  lunar  plains, 
supplemented  by  copious  notes,  and  illustrated  by  a  map  completely 
crowded  with  objects,  some  of  them  very  small  indeed.  As  f^  as 
we  are  able  to  judge,  it  is  quite  a  model  production.  It  also  con- 
tains a  very-  interesting  examination  of  Schroter's  drawings  of  the 
region,  and  a  comparison  of  them  with  recent  photograms  and  ^e 
present  appearance  of  the  plain. 

Uipparchus  is  the  subject  of  another  masterly  monograph,  illus- 
trated by  a  well-eugraved  map,  accompanied  by  a  full  catalogue  of 
objects  and  numerous  descriptive  notes,  together  with  a  comparison 
of  the  region  on  different  photograms.  The  scale  of  the  map  is 
100  inches  to  the  moon's  diiuneter.  We  notice  that  the  paging  of 
the  letterpress  of  Bipparchtu  runs  on  from  that  of  ihe  Mare  Sere-- 
nitatis,  from  which  we  suppose  other  monographs  are  to  follow. 
Certainly  every  lunar  observer  must  hope  that  may  be  the  case ; 
indeed  the  continuance  of  the  areas  of  the  map  is  a  very  desirable 
thing  while  we  have  nothing  at  all  of  the  kina  which  depicts  one 
hundredth  of  the  lunar  features  revealed  by  the  average  telescope 
now  in  the  hands  of  amateurs.  Beer  and  Madler's  map  was  a 
worthy  work  in  1837 ;  but  nearly  forty  years  have  brought  about 
great  improvements  in  instruments  tor  the  purpose  of  observa- 
tion, and,  as  it  seems  to  us,  a  map  which  would  bring  sel^io- 
Rraphy  more  nearly  level  with  the  times  is  really  an  important 
desideratum. 

Following  the  three  maps  to  which  we  have  referred,  we  have 
specimens  of  the  Catalogue  of  Lunar  Objects  according  to  ihe  plan 
originally  devised  by  lkj&.  Birt.  This  catalogue  certiunly  has  the 
merit  of  clearness  and  conciseness ;  and,  by  means  of  a  most  useful 
accompanying  table  of  references  and  synonyms,  the  student  is  able 
easily  to  compare  the  notes  of  difEerent  observers  and  authors  on 
each  particular  locality  which  may  be  under  discussion.  This  is  a 
valuable  adjunct  to  the  descriptive  notes  and  illustrations.  What 
oiur  star-catalogues  are  to  stdlar  observers,  that  would  Mr.  Birt's 
projected  work  be  to  students  of  the  moon,  if  it  were  only  carried 
out  to  completion.  The  method  of  arrangement  adopted  through- 
out all  Mr.  Birt's  productions  seems  to  be  a  specialite  of  his  own. 
Other  works  on  the  moon  mo  could  name,  written  in  what  is  called 
the  popular  style,  and  illustrated  by  excellent  pictorial  representa- 
tions of  the  general  character  of  the  lunar  surface ;  but  from  all 


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Royal  SoeUiy.  143 

tiieae,  which  Are  more  suited  to  the  general  reader,  the  Ydame  be- 
fore us  differs  in  kind ;  and  those  who  desire  to  be  reaUy  acquainted 
wit^  ihs  pumUer  detail*  of  the  yarious  regions  treated  of  will  find 
that  Mr.  Birf  s  work  treats  of  these  especaally •  Herein  it  is  unique, 
and  contains  a  mass  of  yaluable  information  to  be  met  with,  so  far 
as  we  know,  in  no  other  work  extant.  Indeed  all  Mr.  Birt's  maps 
and  notes  are  distinguished  bj  a  painstaking  accuracj  that  will  con- 
fer upon  them  great  value  shoula  another  case  arise  similar  to  that 
of  LiiiiU  in  any  of  the  areas  already  completed ;  for  there  will  be 
found  every  known  spot,  streak,  craterlet,  or  other  feature  de- 
scribed, and  often  distinctly  illustrated;  so  that,  so  far  as  this 
work  is  concerned,  no  future  selenographer  will  be  likely  to  be 
misled. 

Anotiier  portion  of  the  volume  is  occupied  by  two  series  of 
papers,  entiued  '*  Selections  from  the  Portfolios  of  the  Editor  ot 
the  Lunar  Mf^  and  Catalogue/'  in  the  preparation  of  which  Mr. 
Birt  has  been  assisted  by  gentlemen  who  have  given  scnne  attention 
to  selenography,  and  in  which  will  be  found  many  very  interesting 
papers.  EspeciaUy  noticeable  is  one  by  the  Bev.  T.  W.  Webb, 
•«  On  the  Study  of  Change  in  the  Lunar  Surface,"  and  another  by 
Messrs.  Webb  and  Birt  on  the  formation  named  Cleomede$.  The 
latter  contains  formula  for  computing  the  length  of  a  measured 
line  on  the  moon's  surface  in  English  feet,  in  itself  a  really  impox^ 
tant  acquisition  to  every  selenographer.  Many  other  papers,  treat- 
ing of  various  topics,  mil  be  found  suggestive. 

From  a  notice  on  the  wrapper  of  the  second  issue  of  the  '*  Selec- 
tions," we  learn  that  increased  subscriptions  are  required  to  con- 
tinue them.  But  we  cannot  suppose  that  the  want  of  subscriptions 
is  dependent  upon  any  inferiority  in  the  work  itself,  but  rather  on 
its  being  not  generally  known  amongst  astronomers,  and  also  on 
the  absence  of  an  interest  in  the  study  of  the  moon's  surface,  which 
contrasts  so  remarkably  with  the  assiduity  with  which  amateurs 
prosecute  their  studies  in  other  branches  of  astronomy.  We  there- 
fore hope  that  before  long  we  shall  be  called  upon  to  notice  a  f ur^ 
ther  contribution  to  selenography  by  Mr.  Birt. 


XXIV..  Proceedings  qf  Learned  Socieiiei. 

ROYAL  SOCIETY. 
[Continued  from  p.  720 

January  29,  1874. — Joseph  Dalton  Hooker,  O.B.,  President,  in 
the  Chair. 
'^PHE  following  communication  was  read: — 
-•-     "  On  the  Comparative  Value  of  certain  Geological  Ages  (or 
groups  of  formations)  considered  as  items  of  Geological  Time." 
Bj  A.  C.  Eamsay,  LL.D.,  V.P.E.S. 

The  author    first  renews  briefly  several  methods  by  which 
attempts  have  been  made  to  estimate  the  value  of  minor  portions 


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'  144  Royal  Society : — ^Prof.  A.  C.  Ramsay  on  the 

of  geological  time,  such  as: — calculations  intended  to  estimate 
the  age  of  deltas,  founded  on  the  annual  rate  of  accumulation 
of  semments  ;  the  astronomical  method  foUowed  by  Mr.  Croll,  in 
connexion  with  the  recurrence  of  glacial  epochs;  the  relative 
thicknesses  of  different  formations;  and  the  relation  of  strong 
unconformity  between  two  sets  of  formations  in  connexion  with 
marked  disappearance  of  old  genera  and  species,  and  the  appear- 
ance of  newer  forms.  Having  shown  that  none  of  these  metliods 
give  any  clear  help  in  the  absolute  measurement  of  time  in  years 
or  cycles  of  years,  even  when  founded  on  well-established  facts,  he 
proceeds  to  attempt  to  estimate  the  comparative  value  of  long  por- 
tions of  geological  time,  all  of  which  are  represented  by  im- 
portant series  of  formations. 

The  author  then  alludes  to  the  subject  of  two  papers  by  himself, 

S'ven^  to  the  Geological  Society  in  1871,  on  the  Red  Rocks  of 
ngland,  in  which  he  attempted  to  show  that  the  Old  Red  Sand- 
stone, Permian,  and  New  Red  series  were  all  deposited  in  great 
inland  lakes,  fresh  or  salt ;  and  this,  taken  in  connexion  with  the 
wide-spreading  terrestrial  character  of  much  of  the  Carboniferous 
series,  showed  that  a  great  continental  age  prevailed  over  much 
of  Europe  and  in  some  other  regions,  from  the  close  of  the  Silu- 
rian epoch  to  the  close  of  the  Trias.  He  then  endeavours  to  show 
the  value  of  the  time  occupied  in  the  deposition  of  the  above- 
named  formations,  when  compared  \iith  the  time  occupied  in  the 
deposition  of  the  Cambrian  and  Silurian  strata,  and  of  the  marine 
and  freshwater  strata  which  were  deposited  between  the  close  of 
the  Triassic  epoch  and  the  present  day. 

After  alluding  to  the  probable  mixed  estuarine  and  marine  cha- 
racter of  the  purple  and  grey  Cambrian  rocks  of  St.  David's,  it  is 
shown  that  the  Cambrian  and  Silurian  series  may  be  massed  into 
three  great  groups : — first,  from  the  bottom  of  the  purple  Cambrian 
rocks  to  the  top  of  the  Tremadoc  slates ;  these  being  succeeded 
iinconformably  by  the  second  group,  the  Llandeilo  and  Bala  or 
Garadoc  beds ;  on  which  rest  unconformably  the  members  of  the 
third  series,  ranging  from  the  base  of  the  Upper  Llandovery  to 
the  top  of  the  Upper  Ludlow  beds, — each  imconformable  break 
in  stratigraphical  succession  being  accompanied  by  a  correspcnding 
break  in  paiseontological  succession. 

These  three  great  divisions  are  next  shown  to  be  comparable, 
in  the  time  occupied  for  their  deposition,  to  the  three  divisions 
of  Lower,  Middle,  and  Upper  Devonian  rocks,  which  are  consi- 
dered to  be  the  marine  representatives  of  the  Old  Red  Sand- 
stone ;  and  therefore  it  follo\*'s  that  t?ie  time  oc^mpied  in  the  depo- 
aition  of  the  latter  may  have  been  as  long  as  that  taken  in  the  deposition 
of  the  Cambrian  and  Silurian  series.  This  position  is  strengthened 
by  the  great  palfiBontological  differences  in  the  fossils  of  the  Upper 
Ludlow  and  those  of  the  marine  Carboniferous  series,  which  seem 
to  indicate  a  long  lapse  of  time  during  which,  in  Old  Red  Sandstone 
areas,  no  direct  sequence  of  marine  deposits  took  place. 

The  next  question  considered  is,  what  relation  in  point  of  time 


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Comparaiive  Value  of  certain  Geological  Affei.  145 

the  depositioii  of  the  Old  Bed  Sandstone  may  have  taken,  when 
compiled  with  the  time  occupied  in  the  deposition  of  certain 
members  of  the  Mesozoic  formations.  Through  a  series  of  argu- 
ments, lithological,  stratigraphical,  and  pal»ontoiogical,  the  oondu* 
sion  is  arrived  at,  that  the  whole  of  the  Liassic  and  Oolitic  series 
present  the  various  phases  of  one  fades  of  miurine  life,  and,  in  tiiis 
respect,  are  comparable  to  the  changes  in  the  fossil  contents  of  the 
various  subformations  of  the  Cambrian  and  Lingula-flag  series, 
of  which  the  Tremadoc  Slates  form  an  upper  meml^r.  In 
like  manner  the  Lias  and  Oolites  may  be  compared  with  the 
Lower  Devonian  strata ;  and  therefore  a  lower  portion  of  the  Old 
Red  Sandstone  may  have  taken  as  long  for  its  deposition  as  the  whole 
of  the  time  occupied  in  the  deposition  of  the  Jurassic  series. 

Following  out  this  train  of  argument  through  the  Neoccnnian 
and  Cretaceous  strata,  the  result  is  arrived  at  tlMt  the  whole  of 
the  time  occupied  in  the  deposition  of  the  Old  Red  Sandstone  may 
have  been  equal  to  the  whole  of  the  time  occupied  in  the  deposition 
of  aUthe  Jurassic,  WeaMen,  and  Cretaceous  strata  collectively. 

In  the  same  manner  the  next  term  of  the  Continental  era,  tha 
Carboniferous  epoch,  is  compared  with  the  Eocene  period,  both 
being  locally  of  marine,  estuarine,  freshwater,  and  terrestrial 
origin,  and  both  connected  with  special  continental  epochs.  Next 
comes  the  Permian  series,  comparable  in  its  lacustrine  origin  to 
the  Miocene  strata  of  so  much  of  Eur(^,  though  in  the  case  of 
the  Permian  watery  the  lakes  were  salt.  After  this  the  Triassic 
series  of  Europe  alone  remains  of  the  old  continent,  the  maiine 
and  salt-4ake  strata  of  which  are  not  likely  to  have  taken  a  shorter 
time  in  their  deposition  than  the  older  Pliocene  strata. 

If  the  foregoing  method  be  of  value,  we  arrive  at  the  general  con- 
clusion that  the  great  local  continental  era,  which  began  voith  the  Old 
Red  Sandstone  ami  closed  with  the  New  Red  Marl,  is  comparable,  in 
point  of  Geological  Time,  to  that  occupied  in  the  deposiUon  of  the  whole 
of  the  Mesozoic  series  later  than  the  New  Red  Marl,  and  of  all  the  Cai- 
nozoic  formations,  and,  nufre  probably,  of  all  tlie  tims  that  has  elapsed 
since  ^  beginning  of  the  deposition  of  the  Lias  down  to  tJie  present 
day;  and  consequently  the  more  modem  continental  era,  which 
locally  began  with  the  Eocene  period  and  lasts  to  the  present  day, 
has  been  of  much  shorter  duration. 

The  author  then  pointed  out  that  during  the  older  continental 
era  there  flourished  two  typical  floras — one  extending  from  the 
time  of  the  Old  Bed  Sandstone  to  the  close  of  the  Permian  strata ; 
while  the  second,  which  is  largely  of  Jurassic  type,  characterized 
the  Triassic  formations.  From  the  time  of  the  Lias  onward  in 
time,  we  have  also  two  distinct  typical  floras — ^the  first  of  Jurassic, 
and  the  second  of  much  more  modern  type,  beginning  with  the 
Upper  Cretaceous  strata  of  Aix-la-Chapelle  and  lasting  to  the  pre- 
sent day. 

In  like  manner  the  faunas  connected  with  the  land  resolve  them- 
selves into  two  types : — ^the  first  chiefly  Labyrinthodontian,  as  shown 
in  the  Carboniferous  and  Permian  strata ;  and  the  second  charac- 

Phil.  Mag.  S.  4.  Vol.  48.  No.  316.  Aug.  1874.  L 


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146    Royal  Sociehj : — ^Piof,  0.  Eeyiu)lda  on  Surface-forces 

twiBiic  of  ihe  Tzias,  vith  [Crocodilift,  many  land-lkards,  Aiiomo- 
doDtia,  Deinosauria,  and  Marsupial  MaHunalia.  This  buna,  as 
regards  genera,  with  the  exception  of  Labynnthodontia  and  the 
appearanoe  of  Fterosauiia,  is  represented  through  the  remaining 
members  of  the  Mesosoic  formations,  from  Jurassic  to  Creta- 
ceous indusive.  After  this  comes  the  Pachydermatous  Mammalian 
Eocene  fauna,  and  after  ihaJb  the  Miocene  land-fauna,  which, 
in  its  main  diaracters,  is  of  modem  type.  From  Jurassic  to  Cre- 
taceous times,  indusively,  there  was  therefore,  as  far  as  we  know, 
in  this  area  a  land-&una  chiafly^Be^tilian,  iSaurian,  and  Marsupia], 
and  in  Tertiary  times  diiefly  Beptilian  and  PlaoenUl.  (Illusianted 
b^  a  Table.) 

In  conclusion,  the  recent  character  c^  the  early  nuucine  faunas 
of  the  Cunbrian  and  lingula-fleg  series  was  pcMnted  out,  such 
as  Spongida,  Annelida,  Ediinodermata,  Crustacea,  Polyioa,  Bra* 
dnopoda,  Lsmellibram^iata,  Pteropoda,  Nudeobranobiata,  and  Ce- 
phalopoda. This  was  kmg  ago  insisted  on  by  Professor  Huxley ; 
and  we  find  no  evidence  of  its  having  lived  near  the  beginning 
ci  the  zoological  series;  for  below  the  Cambrian  series  we  fure 
at  once  involved  in  a  sort  of  duios  of  metamorphic  strata.  Of 
tbe  geological  history,  in  the  words  oi  Darwin,  '*  we  possess  the 
last  volume  alone,  rdating  only  to  two  or  three  countries.^  The 
connexion  of  this  question  with  that  of  the  comparative  value  oi 
different  geological  eras  is  obvious,  especially  in  rdation  to  the 
palieontological  part  of  the  question. 

June  18. — Joseph  Daltim  Hooker,  C.B.,  President,  in  the  Chair. 

The  following  communication  was  read : — 

*\0a  the  Forces  caused  by  Ev^)oration  from,  and  Cond^isation 
at,  a  Surface."  By  Prof.  Osborne  Beyndds,  of  Owais  College, 
Manchester. 

It  has  been  noticed  by  several  philosophers,  and  particularly  by 
Mr.  Crookes,  that,  under  certain  cuxnimstances,  hot  bodies  appear  to 
repel  uid  cold  ones  to  attract  other  bodies.  It  is  my  object  m  this 
paper  to  pdnt  out,  and  to  describe  experiments  to  prove,  that 
liiese  effects  are  the  results  of  evaporation  and  condensation,  and 
that  they  are  valuable  evidence  of  the  truth  of  the  kinetic  theory 
of  gas,  viz.  that  gas  consists  of  separate  molecules  moving  at  great 
velocities. 

The  experiments  of  whidi  the  explanation  will  be  given  vrere  as 
f dlows : — 

A  light  stem  of  glass,  with  pith-balls  on  its  ends,  was  suspended 
by  a  silk  thread  in  a  glass  flask,  so  that  the  balls  were  nearly  at 
the  same  level.  Some  water  was  then  put  in  the  flask  and  boiled 
until  all  the  air  was  driven  out  of  the  flask,  which  was  then  corked 
and  allowed  to  cod.  When  cold  there  was  a  partial  vacuum  in 
it,  the  gauge  showing  from  |  to  |  of  an  inch  pressure. 

It  was  now  found  that  when  the  flame  of  a  lamp  was  brought 
near  to  the  flask,  the  pith-ball  which  was  nearest  the  flame  was 
driven  away,  and  ihat  with  a  piece  of  ice  the  pith  was  i^tracted« 


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caused  by  Evaporation  and  Con4en$aiion.  147 

This  expenment  wm  rroeated  under  a  rmety  of  drcomstances, 
in  dilEeient  Badk»  and  with  different  balaxioes,  the  stem  bmngiome- 
times  of  glass  and  sometimes  of  platamun ;  the  results,  howeyer, 
were  the  same  in  all  cases,  except  such  variations  as  I  am  about  to 
describe. 

The  pith-balls  were  more  sensitive  to  the  heat  and  oM  when  the 
flask  was  cold  and  the  tension  within  it  low ;  but  the  effect  was 
perceptible  until  the  gauge  showed  about  an  inch,  and  even  after 
that  the  ice  would  attract  the  ball. 

The  reason  why  ^e  repulsion  from  heat  was  not  apparent  at 
greater  tensions,  was  deaiiy  due  to  ihe  convection-currentB  which 
the  heat  generated  within  the  flask.  When  there  was  ^lough 
vapour,  these  currents  carried  the  pith  witli  them ;  they  were,  in 
&ct,  then  sufficient  to  overcome  the  forces  which  otiierwise  moved 
the  pith.  This  was  shown  by  the  fact  that  when  the  bar  was 
not  quite  level,  so  that  one  ball  was  higher  than  the  other,  th6 
curr^its  affected  them  in  different  degrees ;  also  that  a  different 
eSeet  could  be  produced  by  raising  or  lowering  the  position  of  the 
flame. 

The  condition  of  the  pith  also  perceptibly  affected  the  sensitive- 
ness of  the  balls.  When  a  piece  of  ice  was  placed  against  the  side 
of  the  glass,  the  nearest  of  the  pith-balls  would  be  £awn  towards 
the  ice,  and  would  eventually  stop  opposite  to  it.  If  allowed  to 
remain  in  this  condition  for  some  time,  the  vapour  would  con- 
dense on  the  ball  near  the  ice,  while  the  other  \M  would  become 
dry  (this  would  be  seen  to  be  the  case,  and  was  also  shown  by  the 
tipping  of  the  balance,  that  ball  against  the  ice  gradually  getting 
lower).  It  was  then  found,  when  the  ice  was  removed,  that  the 
dry  ball  was  insensible  to  the  heat,  or  nearly  so,  while  that  ball 
which  had  been  opposite  to  the  ice  was  more  than  ordbarily  sen- 
sitive. 

I£  the  flask  were  dry  and  the  tension  of  the  vapour  reduced 
with  the  pump  until  the  gauge  showed  |  of  an  inch,  then,  although 
purely  steiun,  the  vapour  was  not  in  a  saturated  condition,  and 
the  pith-balls  which  were  dry  were  no  longer  sensitive  to  the  lamp, 
although  they  would  still  approach  the  ice. 

From  these  last  two  &cts  it  appears  as  though  a  certain  amount 
of  moisture  on  the  balls  were  necessary  to  render  them  sensitive  to 
the  heat. 

In  order  that  these  results  might  be  obtained,  it  was  necessary 
that  the  vapour  should  be  free  from  air.  If  a  small  quantity 
of  air  was  present,  although  not  enough  to  appear  in  t^e  gaue^e, 
^e  ^ects  rapidly  diminish^,  partictdarly  that  dE  the  ice,  until  nie 
C(mvecti(m-currents  had  it  all  their  own  way.  This  agrees  with  the 
&ct  that  the  presence  of  a  small  quantity  of  air  in  steam  greatly 
retards  condensation  and  even  evaporation. 

With  a  dry  flask  and  an  air-vacuum,  neither  the  lamp  nor  the 
ice  produced  their  effects ;  the  eonvection-currrats  reigned  supreme 
^n  v(^hen  the  gauge  was  as  low  as  |  inch.  Under  these  circum- 
sUno^s  the  lamp  generally  attracted  the  balls  and  the  ice  repelled 

L2 


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148      Roifal  Society  :-*VroL  0.  Reynolds  on  Sw/ace-forces 

them ;  i.  e»  the  curreoits  carried  them  towards  the  lamp  and  from 
the  ice ;  but,  by  placing  the  lamp  or  ice  very  low,  the  reverse  effects 
could  be  obtained,  wfajjch  goes  to  prove  that  they  were  the  effects 
of  the  currents  of  air. 

These  experiments  appear  to  show  that  evaporation  from  a  sur- 
face is  attended  with  a  force  tending  to  drive  the  surface  back,  and 
condensation  with  a  force  tending  to  draw  the  surface  forward. 
These  effects  admit  of  explanation,  although  not  quite  as  simply 
as  may  at  first  sight  appear. 

It  seems  easy  to  omc^ve  that  when  vapour  is  driven  off  from  a 
body  there  must  be  a  certain  reaction  or  recoil  on  the  part  of  the 
body ;  Hero's  engine  acts  on  this  principle.  If  a  sheet  of  damp 
paper  be  held  before  the  fire,  from  that  side  which  is  opposite  to 
the  fire  a  stream  of  vapour  wHl  be  drawn  off  towards  the  fire  wil^ 
a  perceptible  velocity ;  and  therefore  we  can  readily  conceive  that 
there  must  be  a  correspcmding  reaction,  and  that  the  paper  will  be 
forced  back  with  a  force  equal  to  that  which  urges  the  vapour  f or^ 
wards.  And,  in  a  similar  way,  whenever  condensation  goes  on  at 
a  surface  it  must  diminish  the  pressure  at  the  surface,  and  thus 
draw  the  surface  forwards. 

It  is  not,  however,  wholly,  or  even  chiefly,  such  visible  motions  as 
these  that  afford  an  explanation  of  the  phenomena  just  described. 
If  the  only  forces  were  those  which  result  from  the  perceptible 
motion,  they  would  be  insensible,  except  when  the  heat  on  the 
sur&use  was  sufficiently  intense  to  drive  the  vapour  off  with  con- 
siderable velocity.  This,  indeed,  might  be  the  case  if  vapour  had 
no  particles  and  was,  what  it  appears  to  be,  a  homogeneous  elastic 
medium,  and  if,  in  changing  from  liquid  into  gas,  the  expansion 
took  place  gradually,  so  that  the  only  velocity  acquired  by  the  vapour 
was  that  necessary  to  aUow  its  replacing  that  which  it  forces 
before  it  and  giving  place  to  that  which  follows. 

But,  although  it  appears  to  have  escaped  notice  so  far,  it  follows, 
as  a  direct  consequence  of  the  kinetic  tbeory  of  gases,  that,  when- 
ever evaporation  takes  place  from  the  surface  of  a  solid  body  or  a 
liquid,  it  must  be  attended  with  a  reactionary  force  equivalent  to 
an  increase  of  pressure  on  the  surface,  which  force  is  quite  in- 
dependent of  the  perceptible  motion  of  the  vapour.  Also,  conden- 
sation must  be  attended  with  a  force  equivalent  to  a  diminution  of 
the  gaseous  pressure  over  the  condensing  surface,  and  likewise 
independent  of  the  visible  motion  of  the  vapour.  This  may  be 
shown  to  be  the  case  as  follows  : — 

According  to  the  kinetic  theory,  the  molecules  which  constitute 
the  gas  are  in  rapid  motion,  and  the  pressure  which  the  gas  exerts 
against  the  bounding  surfaces  is  due  to  the  successive  impulses  of 
these  molecules,  whose  course  directs  them  against  the  surface,  from 
which  they  rebound  with  unimpaired  velocity.  According  to  this 
theory,  therefore,  whenever  a  molecule  of  liquid  leaves  the  sur&ce 
henceforth  to  become  a  molecule  of  gas,  it  must  leave  it  with  a 
velocity  equal  to  that  with  which  the  other  particles  of  gas  re- 
bound ;  that  is  to.  say,  instead  of  bebg  just  detached  and  quietly 


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earned  by  Evaporation  and  Condeniation.  140 

passing  off  into  the  gas,  it  must  be  shot  off  with  a  Telocity  greater 
than  that  of  a  cannon-ball.  Whateyer  may  be  the  nature  of  the 
forces  which  give  it  the  velocity,  and  which  consume  the  latent 
heat  in  doing  so,  it  is  certain,  from  the  principle  of  conservation 
of  momentum,  that  they  must  react  on  the  surface  with  a  force 
equal  to  j^hat  exerted  on  the  molecule,  just  as  in  a  gun  the  pressure 
of  the  powder  on  the  breech  is  the  same  as  on  the  shot. 

The  impulse  on  the  surface  from  each  molecule  which  is  driven 
off  by  evaporation  must  therefore  be  equal  to  that  caused  by  the 
rebound  of  one  of  the  reflected  molecules,  supposing  all  the  mo- 
lecules to  be  of  the  same  size ;  that  is  to  say,  since  the  force  of 
rebound  will  be  equal  to  that  of  stopping,  the  impulse  from  a  par- 
ticle driven  off  by  evaporation  will  be  half  the  impulse  received 
from  the  stopping  and  reflection  of  a  particle  of  the  gas.  Thus 
the  effect  of  evaporation  will  be  to  increase  the  number  of  impulses 
on  the  surface ;  and  although  each  of  the  new  impulses  will  only  be 
half  as  effective  as  the  ordinary  ones,  they  will  add  to  the  pressure. 

In  the  same  way,  whenever  a  molecide  of  gas  comes  up  to  a 
Bur&ice  and,  instead  of  rebounding,  is  caught  and  retained  by  the 
surface,  and  is  thus  condensed  into  a  molecule  of  liquid,  the  impulse 
which  it  will  thus  impart  to  the  sur&ce  will  only  be  (me  half  as 
great  as  if  it  had  rebounded.  Hence  condensation  will  reduce  the 
magnitude  of  some  of  the  impulses,  and  therefore  will  reduce  the 
pressure  on  the  condensing  surface. 

For  instance,  if  there  were  two  surfaces  in  the  same  vapour, 
one  of  which  was  dry  and  the  other  evaporating,  then  the  pres- 
sure would  be  greater  on  the  moist  surface  than  on  that  which 
was  dry.  And,  again,  if  one  of  the  surfaces  were  dry  and  the 
other  condensing,  then  the  pressure  would  be  greater  on  the  dry 
surface  than  on  that  which  was  condensing.  Hence,  if  the  opposite 
sides  of  a  pith-ball  in  vapour  were  in  such  different  conditions,  the 
ball  would  be  forced  towards  the  colder  side. 

These  effects  may  be  expressed  more  definitely  as  f oUows : — 

Let  V  be  the  velocity  with  which  the  molecides  of  the  vapour 
move, 

p  the  pressure  on  a  unit  of  sur&u^, 
d  the  weight  of  a  unit  of  volume  of  the  vapour, 
w  the  weight  of  liquid  evaporated  or  condensed  in  a  second ; 
then  the  weight  of  vapour  which  actually  strikes  the  unit  of  dry 
surface  in  a  second  will  be 

dv 

and  the  pressure  p  will  be  given  by 

and/  (the  force  arising  frcnn  evaporation)  will  be  given  by 

-    wv 

*  See  Maxwell,  'Theory  of  Heat»'  p.  294. 


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ISO     Royal  Sodtty ;— Prof.  O.  Reynoldi  on  Sttrfaet-forca 
thorefore 


Thus  we  hare  an  expresBioii  for  the  force  in  terms  of  the  qnaiH 
titj  of  watw  evaporated  and  the  ratio  of  the  pressure  to^the  imf 
Bit  J  of  the  yapour;  and  if  the  heat  neoessary  to  evaporate  the 
liquid  (thd  ktent  heat)  is  known,  we  can  find  the  force  which 
would  result  from  a  given  expenditure  of  heat. 

Applying  these  results  to  steam,  we  find  that,  at  a  tmnperatore 
of  60  ,  the  evaporation  of  1  lb.  of  water  from  a  surfaoe  would  be 
sufficient  to  maintain  a  force  of  65  lbs.  for  one  second. 

It  is  also  important  to  notice  that  this  force  will  be  proportioaial 
to  the  square  root  of  the  absolute  temperature,  and,  oonseqnenily, 
will  be  approximately  constant  between  temperatures  of  32°  and 
212°. 

If  we  take  mercury  instead  of  water,  we  find  that  the  force  is 
only  6  lbs.  instead  of  65  lbs. ;  but  the  latent  heat  of  mercury  is  only 
^  that  of  water,  so  that  the  same  expenditure  of  heat  would  main- 
Uin  nearly  thi-ee  times  as  great  a  force. 

It  seems,  therefore,  that  in  this  way  we  can  g^ve  a  satisfactory 
explanation  of  the  experiments  previously  described.  When  tiiie 
radiated  heat  from  the  lamp  falls  on  the  pith,  its  temperature  will 
rise,  and  any  moisture  on  it  ^vill  begin  to  evaporate  and  to  drive 
the  pith  fro«n  the  lamp.  The  evaporation  will  be  greatest  on  that 
ball  which  is  nearest  to  the  lamp ;  therefore  this  ball  will  be  driven 
away  until  the  force  on  the  other  becomes  equal,  aftei^  which  tiia 
balls  will  come  to  rest,  unless  momentum  carries  them  further. 
On  the  other  hand,  when  a  piece  of  ice  is  brought  near,  the  tem^ 
perature  of  the  pith  will  be  reduced,  and  it  will  condense  the  va* 
pour  and  be  drawn  towards  the  ice. 

It  seems  to  me  that  the  same  explanation  may  be  given  of  Mr. 
Crookes's  experiments ;  for,  although  my  experiments  were  made  on 
water  and  at  comparatively  high  pressures,  they  were  in  realify 
undertaken  to  vemy  the  explanation  as  I  have  given  it.  I  used 
water  in  the  hope  oi  finding  (as  I  have  found)  that,  in  a  conden- 
sable vapour,  tne  results  could  be  obtained  with  a  greater  density 
of  vapour  (that  is  to  say,  with  a  much  less  perfect  vacuum),  the 
elEect  being  a  consequence  of  the  saturated  condition  of  the  vapour 
rather  than  of  the  perfection  of  the  vacuum. 

Mr.  Oookes  only  obtained  his  results  when  his  vacuum  was 
nearly  as  perfect  as  the  Sprengel  pump  would  make  it.  Up  to  this 
point  he  had  nothing  but  the  inverse  effects,  viz.  attraction  with 
neat  and  repulsion  with  cold.  About  the  cause  of  these  he  seems 
to  be  doubtful;  but  I  venture  to  think  that  they  may  be  entirely 
explained  by  the  expansion  of  the  surrounding  gas  or  vapour,  and 
the  consequent  oonveotion-cun^ents.  It  must  be  remembered  that 
whenever  the  air  about  a  ball  is  expanded,  and  thus  rendered 
lighter  by  heat,  it  will  exercise  less  supporthig  or  floating  power 
on  the  ball,  which  will  therefore  tend  to  sink.    This  tendency  will 


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caused  by  Evaporution  and  Condensaiion.  ISl 

be  in  opposition  to  the  lifting  of  the  Mcendinc  current,  and  it  will 
depend  on  the  slwpe  and  thickness  of  the  hsS  whether  it  will  rise 
or  fall  when  in  an  ascending  enrrent  of  heated  gas. 

The  reascn  why  Mr.  Crookes  did  not  obtain  the  same  results 
with  a  less  iperte(A>  Taoanm  was  because  he  had  then  too  large  a 
proportion  of  air,  or  non-condensing  gas,  mixed  with  the  Tapour, 
whM^h  i^so  was  not  in  a  state  of  satimition.  In  bis  experiments 
the  condensable  raponr  was  that  of  mercurj,  or  something  whidi 
required  a  siill  higher  temperature,  and  it  was  necessary  thi^  the 
Tacnam  should  he  ybtj  perfect  for  such  Tapour  tp  be  any  thing 
like  pure  and  in  a  satmrated  condition.  As  soon,  howerer,  as  this 
state  of  perfection  was  reached,  then  the  effects  were  more  appa* 
rent  than  in  the  corresponding  ease  of  water.  This  agrees  well 
with  the  explanation ;  for,  as  preriously  shown,  the  effect  oi  mercury 
would,  for  the  same  quantity  of  heat,  be  three  times  as  great  as 
that  of  water ;  and,  besides  this,  the  perfect  state  of  the  vacuum 
would  oUow  the  pith  (or  whateyer  the  ball  might  be)  to  move  much 
more  freely  than  when  in  the  vapour  of  water  at  a  considerable 
tension. 

Of  course  this  reasoning  is  not  confined  to  mercuiy  and  water ; 
any  gas  which  is  conden»Bd  or  absorbed  by  the  balls  when  cold 
in  greater  quantities  than  when  worm  would  give  the  same  re- 
sults ;  and,  as  this  property  appears  to  belong  to  all  gases,  it  is 
only  a  question  of  bringing  the  vacumn  to  the  right  degree  of 
tension. 

There  was  one  fact  connected  with  Mr.  Crookes's  experiments 
which,  independently  of  the  previous  considerations,  led  me  to  the 
conclusion  that  the  result  was  due  to  the  heating  of  the  pith,  and 
was  not  a  direct  result  of  the  radiated  heat. 

In  one  of  the  experiments  exhibited  at  the  Soir^  of  the  Boyal 
Society,  a  candle  was  placed  close  to  a  flask  containing  a  bar  of 
pith  suspended  from  the  middle :  at  first,  the  only  thing  to  notice 
was  that  the  pith  vras  oscillating  considerably  under  the  action  of 
the  candle ;  each  end  of  the  bar  alternately  approached  and  receded, 
showing  that  the  candle  exercised  aninfiuenoe  similar  to  that  which 
might  have  been  exercised  by  the  torsion  of  the  thread  had  this  been 
stiff.  After  a  few  minutes'  observation,  however,  it  became  evi- 
dent that  the  oscillations,  instead  of  gradually  diminishing,  as  one 
naturally  expected  them  to  do,  continued ;  and,  more  than  this,  they 
actually  increased,  until  one  end  of  the  bar  passed  the  light,  after 
which  it  seemed  quieter  for  a  little,  though  the  osciUaticms  again 
increased  until  it  again  passed  the  light.  As  a  great  many  people 
and  lights  were  moving  about,  it  seemed  possible  that  this  might 
be  due  to  external  disturbance,  and  so  its  full  importance  did 
not  strike  me.  Afterwards,  howe\  er,  I  saw  that  it  was  only  to  bo 
explained  on  the  ground  of  the  force  being  connected  with  the 
temperature  of  the  pith.  During  part  of  its  swing  one  end  of  the 
pith  must  be  increasing  in  temperature,  and  during  the  other  part 
it  must  be  cooling.  JiJid  it  is  easily  seen  that  the  ends  will  not  be 
hottest  when  nearest  the  light^  (xr  coldest  when  furthest  away ;  they 


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152.  Royal  Society. 

will  acquire  heat  for  some  time  after  they  have  begun  to  reeede,  and 
lose  it  aft^r  they  have  begun  to  approach.  There  will,  in  fact,  be 
a  certain  lagging  in  the  effect  of  the  heat  on  the  pith,  like  that 
which  is  apparent  in  the  action  of  the  sun  on  a  comet,  which  causes 
the  comet  to  be  grandest  after  it  has  passed  its  perihelion.  From 
this  cause  it  is  easy  to  see  that  the  mean  temperature  of  the  ends 
will  be  greater  during  the  time  they  are  retiring  than  while  i^- 
preaching,  and  hence  the  driving  force  on  that  end  which  is  leaving 
will,  on  the  whole,  more  than  balance  the  retarding  force  on  that 
which  is  approaching ;  and  the  result  will  be  an  acceleration,  so  that 
the  bar  will  swing  further  each  time  until  it  passes  the  candle,  after 
which  the  hot  side  of  the  bar  will  be  opposite  to  the  light,  and  will 
for  a  time  tend  to  counteract  its  effect,  so  that  the  bar  will  for  a. 
lame  be  quieter.  This  fact  is  independent  evidence  as  to  the  nature 
of  the  force ;  and  although  it  does  not  show  it  to  be  evi^ration, 
it  shows  that  it  is  a  force  depending  on  the  t^operature  of  the  pith, 
and  t^at  it  is  not  a  direct  result  of  radiation  from  the  candle. 

Since  writing  the  above  paper,  it  has  occurred  to  me  that,  accord- 
ing to  the  kinetic  theory,  a  somewhat  similar  effect  to  that  of  eva- 
poration must  result  whenever  heat  is  communicated  from  a  hot 
surface  to  gas. 

The  particles  which  impinge  on  the  surface  will  rebound  with  a 
greater  velocity  than  that  with  which  Ithey  approached ;  and  con- 
sequently the  effect  of  the  blow  must  be  greater  than  it  would  have 
been  had  the  surface  been  of  the  same  temperature  as  the  gas. 

And,  in  the  same  way,  whenever  heat  is  communicated  from  a 
gas  to  a  surface,  the  force  on  the  surface  will  be  less  than  it  other- 
wise would  be,  for  the  particles  will  reboimd  with  a  less  velocity 
than  that  at  which  they  approach. 

Mathematically  the  result  may  be  expressed  as  follows — the 
symbols  having  the  same  meaning  as  before,  e  representing  the 
energy  communicated  in  the  form  of  heat,  and  Sv  the  alteration 
which  the  velocity  of  the  molecule  undergoes  on  impact.  As  before, 

p=_ort;=V   -d' 

Therefore,  in  the  case  of  steam  at  a  temperature  of  60^, 

•^     2000 
and  in  the  case  of  air 

/as— L. 

•'''1400" 


and 


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Geological  Society.  l53 

It  must  be  remembered  that  c  depends  on  the  rate  at  which 
cold  particles  will  come  up  to  the  hot  surface,  which  is  very  slow 
when  it  d^nds  only  on  the  diffusion  of  the  particles  of  the  gas 
infer  se  and  the  diffusion  of  the  heat  amongst  them. 

It  will  be  much  increased  by  convection-currents;  but  these 
wiU  (as  has  been  already  explained),  to  a  certain  extent,  produce 
an  opposite  effect.  It  would  also  seem  that  this  action  cannot  have 
had  much  to  do  with  Mr.  Crookes's  experiments,  as  one  can  hardly 
conceive  that  much  heat  could  be  communicated  to  the  gas  or  va- 
pour in  such  a  perfect  vacuum  as  that  he  obtained,  unless,  indeed, 
the  rate  of  diffusion  varies  inversely  as  the  density  of  a  gas*.  It 
wiD  be  interesting,  however,  to  see  what  light  experiments  will 
throw  on  the  question. 

GEOLOGICAL  SOCIETT. 

[Continued  from  p.  76.] 

November  5,  1873.— Prof.  Eamsay,  F.R.8.,  Vice-President, 

in  the  Chair. 

The  following  communications  were  read : — 

1.  "On  the  Skull  of  a  Species  of  IlalitTierium  from  the  lied  Crag 
of  Suffolk."     By  Prof.  W.  H.  Flower,  F.R.S.,  F.G.S. 

The  specimen  described,  which  is  in  the  collection  of  the  Rev.  H. 
Canham,  ofWaldringfield,  is  from  the  so-called  coprolito-  or  bone-bed 
at  the  bnse  of  the  Red  Crag,  and  presents  the  usual  aspect  of  the 
mammalian  remains  from  that  bod.  It  is  of  especial  interest  as 
furnisliina:  Iho  first  recorded  cvideuce  of  llie  existence  in  Britain  of 
animals  belonging  to  the  order  Sircnia.  The  fmgracnt  consists  of 
the  facial  part  of  the  cranium,  separated,  probably  before  fossiliza- 
tioc,  from  the  posterior  part  at  the  fron to-parietal  suture,  and  in  a 
line  descending  vertically  therefrom.  It  was  afterwards  subjected 
to  severe  attrition,  by  which  many  of  the  projecting  parts  have  been 
removed  ;  but  sufficient  remains  to  enable  its  general  relationship  to 
known  forms  to  be  determined.  The  whole  of  that  portion  of  the 
maxillsc  in  which  the  molar  teeth  were  implanted  is  preserved. 

The  author  compared  the  fossil  skull  with  those  of  the  existing  and 
extinct  spedes  of  the  order,  and  stated  that,  while  it  presents  many 
characters  common  to  the  Manati  and  the  Dugong,  there  are  others 
by  which  it  differs  from  both,  the  most  striking  being  the  more 
normal  development  of  the  nasal  bones  and  the  outer  wall  of  the 
nasal  fossie,  and  especially  the  dentition,  in  all  of  which  it  shows  a 
more  generalized  condition.  The  existence  in  it  of  maxillary  teeth 
removes  it  still  further  from  Bhytina,     In  general  character  the 

*  June  10. — ProfesKor  Maxwell  has  shown  that  the  diffusion  both  of  heat 
and  of  the  gas  varies  inversely  as  the  density;  therefore,  excepting  for  con- 
vection-currents,  the  amount  of  heat  communicated  from  a  surface  to  a  gas 
would  be  independent  of  the  density  of  the  gas,  and  hence  the  force /would  be 
independent  of  the  density;  that  is  to  say,  this  force  woidd  remain  constant 
as  the  vacuum  improyed,  while  the  convection-currents  and  counteracting 
forces  would  gradually  diminish.  It  seems  probable,  therefore,  that  Mr. 
Crookes's  results  are,  at  least  in  part,  due  to  this  force. 


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164  0$ohgkal  SoeUiy  ;— 

molars  eorrespond  with  those  of  the  genus  HdUAsrkam^  in  which 
the  anthor  oonsiclered  that  this  fossil  found  its  nearest  ally  in  if. 
Schitm,  Kaup,  from  the  Miooene  of  the  Bhine  YaUeyi  a  fbnnaticm 
inwhidi  several  of  the  animals  of  the  Bed-Crag  bone*hed  are  known 
to  oocur.  The  difPerenoes,  however,  espeoiallj  the  larger  sue  of  the 
eranium,  in  the  Crag  specimen^  and  the  larger  size  of  its  teetb> 
induce  the  author  to  regard  it  as  a  diitinot  species,  which  he  pro- 
poses to  name  HalUhsrium  Canhamu 

2,  "  New  Facts  hearing  on  the  Inquiry  concerning  Forms  inter- 
mediate between  Birds  and  Beptiles."  By  Henry  Woodward,  Esq., 
P.B.S.,  F.as. 

The  author,  after  giving  a  brief  sketch  of  the  Sauropsida,  and 
referring  especially  to  those  points  in  which  the  Pterosaurians 
approach  and  differ  from  birds,  spoke  of  the  fossil  birds  and  land 
reptiles  which  he  considered  to  link  together  more  closely  the 
Sauropsida  as  a  dass. 

The  most  remarkable  reoent  discoreries  of  fossil  birds  are  :-* 

I.  ArchceopUryx  macrura  (Owen),  a  Kesozoic  type,  which  has  a 
peculiar  reptilian-like  tail,  composed  of  twenty  free  and  apparently 
unanohylosed  cylindrical  vertebr«D,  each  supporting  a  pair  of  quill- 
feathers,  the  last  fifteen  vertebne  having  no  transverse  processes, 
and  tapering  gradually  to  the  end. 

II.  Ichthyomis  dispar  (Marsh),  discovered  by  Prof,  0.  C.  Marsh 
in  1872  in  the  Upper  Cretaceous  beds  of  Kansas,  XT.  S.  It  possessed 
well-developed  teeth  in  both  jaws.  The  teeth  are  set  in  distinct 
sockets,  and  are  all  more  or  less  inclined  backwards. 

m.  Odontopteryx  iolmpica  (Owen),  an  Eocene  bird  from  the 
London  Clay  of  Sheppev,  the  skull  of  which  alone  has  been  dis- 
covered, has  very  prominent  denticulations  of  the  alveolar  margins 
of  the  jaws. 

The  author  then  referred  to  the  Dinosauria,  some  of  whidi  he 
considered  to  present  points  of  structure  tending  towards  the  so- 
called  wingless  birds. 

I.  CompiOQWiikM  hiigipes  (A.  Wagner),  from  the  Oolite  of  Solon- 
hofen,  is  about  two  feet  in  length,  having  a  small  head  with  toothed 
jaws,  suDDorted  on  a  long  and  slender  neck. 

The  iliac  bones  are  prolonged  in  front  of  and  behind  the  aceta- 
bulum ;  the  pubes  are  long  and  slender.  The  bones  of  the  fore 
limbs  are  small,  and  were  probably  furnished  with  two  clawed 
digits.  The  hind  limb  is  very  large,  and  disposed  as  in  birds,  tlie 
femur  being  shorter  than  the  tibia.  The  proximal  division  of  the 
tarsus  is  anchylosed  with  the  tibia  as  in  birds. 

II.  The  huge  carnivorous  Megcdosaurus,  ranging  from  the  Lias  to 
the  Wealden,  had  strong  but  not  masslTe  hind  limbs,  and  short 
reduced  fore  Hmbs ;  it  moved  with  free  steps,  chiefly  if  not  solely 
on  its  hind  Umbs,  which  is  trua  also  rf  the  vegetable-eating  lisarcb 
of  the  Mesoaoio  rooks. 

The  author  next  drew  attOBtiott  to  the  Frilled  Lizard  oi  Australia, 
Cfhlamydifsaurus  Kingxi  (Gray),  which  has  its  fore  Hmbs  very  much 
smaller  than  the  hind  limbs,  and  has  been  observed  not  only  to  sit 


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Mr.  J.  W.  Haike  on  a  very  large  Saurian  Limb-bane.     156 

up  oceasionaQy,  Imt  to  nm  habitoally  upon  tiie  gvovmA  <m  its  bind 
1^;b,  its  fore  paws  not  touching  the  earth,  which  upright  eaiiiage 
neceesitatM  qMcial  mo^ftcations  of  ibe  sacrum  and  palTio  bones. 

The  Solenhofen  limestone,  in  which  Pterosauiia  are  frequent, 
and  which  baa  yielded  the  remains  of  ArehcBopUryx  and  of  Cem-' 
]^$ognaihus^  has  also  furnished  a  slab  bearing  a  bipedal  track,  re- 
sembling what  might  be  produced  by  Chlamydosauru$  or  Comp$o^ 
ffnathue.  It  shows  a  median  track  formed  by  the  tail  in  being  drawn 
along  the  ground ;  on  each  side  of  this  the  hind  feet  with  outspread 
toes  leave  their  mark,  while  the  fore  feet  just  touch  the  ground, 
leaving  dot-like  impressions  nearer  the  median  line.  Hence  the 
author  thought  that,  while  some  of  the  bipedal  tracks  which  are  met 
with  from  the  Trias  upwards  may  be  the  "  spoor "  of  struthious 
birds,  most  of  them  are  due  to  the  bipedal  progression  of  the 
Secondary  Beptiles. 

3.  <*Nota  on  the  Astragalus  otigwtnodon  MawtdU."^  By  JT.  W. 
Holke,  Esq.,  P.B.fl.,  F.G.S. 

The  author  exhibited  and  described  an  astragalus  of  Iguanod&n 
from  the  collection  of  E.  P.  Wilkins,  Esq.,  F.6J9.  The  bone  was 
bdieved  to  be  previously  unknown.  It  is  a  bone  of  iregular  form, 
having  on  its  lower  surface  the  characteristio  pulley-shape  of  a 
movable  hinge-joint  The  upper  surface  presents  a  form  exactly 
adapted  to  that  of  the  distal  end  of  the  tibia ;  so  that  the  applied 
surfaces  of  the  astragalus  and  tibia  must  have  interlocked  in  such  a 
manner  as  to  have  precluded  all  motion  between  them.  The  author 
remarked  upon  the  interest  attaching  to  this  fact  in  connexion  with 
the  question  of  the  relationship  between  the  Dinosauria  and  Birds. 

4.  "  Note  on  a  very  large  Saurian  limb-bone,  adapted  fbr  progres- 
sion upon  land,  from  the  Kimmeridge  Clay  of  Weymouth,  Dorset.*' 
By  J.  W.  Hulke,  Esq.,  F.R.S.,  F.G.S. 

The  bone  described  by  the  author  presents  a  closet  resemblance 
to  the  Crocodilian  type  of  humerus  than  to  any  other  bone ;  and  he 
regarded  it  as  the  left  humerus  of  the  animal  to  which  it  belonged. 
Its  present  length  is  64  inches';  but  when  perfect  it  eould  hardly 
have  been  less  than  68  inches  in  length.  The  middle  of  the  shaft 
is  cylindroid.  Its  transverse  section  is  of  a  subtrigonal  figure,  and 
presents  a  large  coarsely  cancellated  core,  enclosM  in  a  compact 
cortical  ring.  The  bone  is  considerably  expanded  towards  the  two 
extremities ;  the  distal  articular  surf&ce  is  oblong,  and  divided  into 
a  pair  of  condyles  by  a  very 'shallow  vertical  groove;  below,  the 
anterior  border,  in  its  proximal  half,  is  much  wider  than  the  cor- 
responding portion  of  the  posterior  border,  and  is  flattened  and  pro- 
duced downwards  into  a  ventrally  projecting  crest ;  and  tiio  distal  half 
of  this  border  forms  a  thin,  rough  crest,  projecting  forwards.  The 
presence  of  these  crests  distinguishes  the  present  humerus  fh>m 
those  of  Pelorosaufus  and  of  Ceteoeaurus  &a<mien$i8 ;  but  the  general 
correspondence  of  th6  bone  with  the  humerus  of  the  latter  species 
leads  the  author  to  refer  it  provisionally  to  a  species  of  Ceteommrue, 
whicb  he  proposes  to  name  C  hwm^o-irietafus^ 


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[    156    ] 
XXV.  Intelligence  and  Miscellaneous  Articles. 

ON  A  SIMPLE  OCULAR-8FEGTR08COPB  FOR  8TAB8. 
BT  F.  SOLLNEli. 

^rilE  annexed  figure  shows,  of  the  natural  size,  the  section  of  a 
A  compendious  form  of  staivspectroscope  in  combination  with 
the  ocular  of  a  telescope. 

It  consists  of  a  small  direct-vision  prism  fixed  in  a  tube  CD,  the 
dispersion  of  which  is  about 
equivalent  to  that  of  the  sys- 
tem of  prisms  of  a  Browning 
miniature  spectroscope.  The 
tube  C  D  is  movable  in  a  se- 
cond tube,  A  B,  which  can  be 
screwed  upon  the  head  of  the 
eyepiece  and  contains  a  cylin- 
drical lens  L  of  about  100 
millims.  focal  distance.  As 
the  length  of  the  line  of  light 

produced  by  this  lens  depends  both  on  its  focal  distance  and  also 
on  the  dimensions  and  proportions  of  the  optical  parts  of  the  tele- 
scope, it  is  advisable  to  have  in  readiness  several  cylindrical  lenses 
of  different  lengths  of  focus,  so  as  to  be  able  to  employ  them  ac- 
cording to  the  length  of  the  line  of  light  (and  consequently  the 
breadth  of  the  spectrum)  desired. 

0^  and  O^  are  the  two  lenses  of  the  eyepiece,  and  hence  do  not 
belong  to  the  spectroscope. 

If  with  this  instrument  the  spectrum  of  a  star  is  to  be  observed, 
the  tube  C  D  vdth  the  prism  is  first  removed,  and  the  ocular  bo  ar- 
ranged that  when  the  eve  is  at  O  a  sharp  line  of  light  is  seen.  It 
is  essential,  in  doins  this,  that  the  eye  should  be  at  about  the  same 
distance  from  the  lens  L  as  when  the  prism  is  employed.  The 
tube  C  D  is  now  inserted,  in  such  a  manner  that  the  refracting 
edge  of  the  prism  lies,  as  usual,  parallel  to  the  luminous  line,  and 
consequently  the  spectrum  attains  its  greatest  breadth.  Self-evi- 
dently,  for  a  given  telescope,  the  suitable  arrangement  need  only 
be  once  ascertained ;  so  that  then  by  a  small  screw  S  the  prism  can 
be  fixed  in  an  invai;^ble  position  >\ith  respect  to  the  cylindrical 
lens  L.  The  prism  is  manufactured  by  M.  Mens,  of  Munich ;  and 
he  prefers  to  use  it  in  this  compendious  form  for  microscopes. 

The  intensity  of  the  light  of  this  ocular-spectroscope  is  so  consi- 
derable, that,  in  combination  with  a  small  portable  telescope,  the 
objective  of  which  has  only  35  millimetres  aperture  and  about  400 
millims.  focal  distance,  it  shows  distinctly  the  lines  of  stars  of  the 
first  magnitude,  such  as  Wega,  a  Ononis,  and  even  a  Herculis  wJieti 
the  state  of  tJie  atinosphere  corresponds^  as  Professor  Winnecke  and 
Dr.  Yogel  convinced  themselves  and  others  on  the  occasion  of  their 
visit  to  Leipsdg  in  the  course  of  the  past  year.  When  Venus  ap- 
pears as  a  slender  crescent,  its  spectrum  is  singularly  beautiful. 

Although,  according  to  the  well-known  methods  employed  by 


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Intelligence  and  Miscellaneous  Articles.  157 

Browuiug,  Yogel,  and  others,  a  scale  could  be  very  easily  connected 
with  this  instrument,  it  can  be  recommended  even  without  one  for 
systematic  mass-observations  o£  fixed-star  spectra,  in  which  the 
prime  object  is  to  ascertain  the  typical  constitution  o£  the  spectra. 
As  the  essential  differences  between  these  types  probably  depends 
only  on  the  temperature  and  mass  of  those  incandescent  bodies,  and 
according  to  the  observations  of  Secchi  and  others  those  types  stand 
in  a  certain  relation  to  the  distribution  of  the  stars  in  space,  such 
systematically  conducted  mass-observations  may  in  future  become 
of  high  importance  for  the  progress  of  astrophysics. 

I  permit  myself,  in  conclusion,  the  remark  that  the  combination 
above  described  was  explained  and  exhibited  by  me  at  the  last  meet- 
ing of  the  Astronomical  Society  at  Hamburg,  in  September  1873. — 
Berichte  der  Icon,  sdchs.  Oesellschctft  der  Wissenschaften  math.-phys. 
Classe,  April  23,  1874. 

NOTE  ON  THE  CAUSE  OF  TIDES*  BY  £.  J.  CHAPMAN^  PH.D.,  PRO- 
FESSOR OF  MINBBALOOY  AND  OEOLOOT  IN  UNIVERSITY  CO L« 
LEGE^  TORONTO*. 

The  phenomenon  of  the  tides,  stated  broadly,  consists  of  a  pass- 
ing elevation,  real  or  apparent,  of  oceanic  waters  at  two  opposite 
points  on  the  surface  of  the  globe.  These  elevations,  which  follow 
the  moon  in  its  course,  may  become  greatly  intensified  under  local 
conditions,  as  where  opposing  coast-lines  impede  the  progress  of 
the  tidal  wave ;  but  in  the  open  ocean,  it  is  well  known,  they  are 
of  but  slight  significance.  According  to  the  received  theory,  they 
are  occasioned  essentially  by  the  unequal  degree  of  attraction  ex- 
erted by  the  moon  on  different  parts  of  the  earth — this  attraction 
being,  of  course,  modified  by  that  of  the  sun.  It  is  thus  assumed 
that  the  waters,  owing  to  their  comparative  mobility,  are  drawn 
towards  the  moon  on  one  side  of  the  globe,  whilst  the  solid  earth 
is  drawn  away  from  the  waters  on  the  other  side — or,  to  use  the 
common  phraseology,  is  drawn  towards  the  moon  faster  than  the 
waters  can  follow. 

This  view,  although  not  without  opponents,  has  been  almost  uni- 
versally adopted  in  default  of  a  more  satisfactory  explanation. 

The  explBoiation  of  the  cause  of  tides  now  suggested  has  at  least 
this  merit :  it  applies  the  same  principle  in  elucidation  of  both  tides 
— that  nearest  the  moon,  and  that  on  the  opposite  side  of  the  globe. 
It  is  briefly  this : — When  two  bodies  pull  against  each  other,  there 
must  necessarily  be  a  contraction  of  particles  towards  the  centre  of 
each  body  along  the  line  of  pull  or  resistance.  In  the  pull,  there- 
fore, of  the  earth  upon  the  moon,  the  earth  (and  of  course  the  moon 
also)  must  suffer  a  passing  contraction,  the  part  along  the  line  of 
pull,  so  to  say,  contracting  more  than  the  other  parts.  But  this 
contraction  is  mechanical  only,  and  is  therefore  a  compression ;  and 

*  Commiinicated  by  the  Author.  Condensed  from  a  commuDioation 
made  to  the  Canadian  Institute,  February  7,  IS74, 


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158  fnietligence  and  Miscellaneoui  Articles* 

M  water  is  practically  incompressible,  tiie  sea  remains  essentially 
unoffectod,  whilst  the  earth  shrinks  beneath  it,  and  l^us  causes  the 
tide.  The  shrinkage  of  course  becomes  greater,  and  the  tide  higher, 
when  both  sun  and  moon  take  part  in  the  counter-pull,  whether 
acting  on  the  same  side  of  the  eaiih  or  on  opposite  sides.  It  may 
be  assumed,  however,  from  the  known  heignt  of  the  tidal  wave 
where  the  march  of  this  wave  is  unopposed,  that  the  maximum 
amount  of  contraction  does  not  exceed  a  foot  for  each  thousand 
miles  of  the  earth's  radius — being  thus,  in  round  numbers,  less  than 
one  part  in  five  millions.  In  the  tremendous  pull  of  the  earth  upon 
the  moon,  by  which  the  moon  is  kept  upon  its  course,  a  passing 
contraction  of  this  comparatively  slight  amount  may  be  easfly  con- 
ceived to  follow.  According  to  the  commonlv  adopted  theory,  one 
tide  is  assumed  to  result  from  the  withdrawal  of  the  earth,  locally, 
from  the  waters  above  it ;  in  the  view  now  proposed,  both  tides  are 
assumed  (although  on  a  different  principle)  to  be  thus  caused. 


ON  THE  TEMPERATURE  OP  THE  SUN.      BY  J.  VIOLLl. 

Several  months  since,  I  undertook  some  experiments  to  deter- 
mine, by  various  methods,  the  temperature  of  the  sun.  I  beg  the 
Academy  to  kindly  permit  me  to  submit  to  it  the  first  results  St  my 
researches. 

Measurements  of  solar  heat  can  be  made  in  two  ways.  In  the 
first,  a  thermometer  is  placed  successively  during  equal  times  in  the 
shade  and  then  in  i^e  sun,  and  the  course  of  the  instrument  is  folr 
lowed  in  each  case :  this  is  the  dynamic  methody  that  of  the  pyrohe- 
liometer  of  Pouillet.  In  the  second  the  thermometer  remains  sub- 
mitted to  solar  radiation  until  the  temperature  indicated  by  the 
instrument  becomes  stationary ;  and  at  tne  same  time  the  tempe- 
rature of  the  thermometer  and  that  of  the  enclosure  are  noted:  this 
is  the  static  method,  that  which  appears  to  be  adhered  to  by  most 
ot  the  physicists  who  occupy  themselves  with  the  measurement  of 
solar  heat.  I  shall  for  the  moment  speak  only  of  the  latter  me- 
thod, and  in  the  first  place  copsider  its  principle. 

Let  a  spherical  envelope  be  maintained  at  a  constant  temperature 
i,  and  let  the  bulb  of  a  thermometer  be  in  i^e  centre  of  the  sphere, 
which  bulb  I  will  for  an  instant  suppose  infinitely  small.  The  en- 
closure is  coated  with  lampblack,  as  well  as  the  bulb  of  the  thermo- 
meter. Let  us  suppose  equilibrium  of  temperature  established. 
The  enclosure  then  sends  to  the  thermometer  a  quantity  of  heat  Sa<, 
a  being  Dulong's  constant  or  1*0077 ;  and  the  thermometer  sends 
back  to  the  enclosure  the  same  quantity  of  heat  Sa^  Let  us  now 
pierce  in  the  spherical  enclosure  a  circular  aperture  w  of  such  di- 
mensions that  it  will  be  seen  from  the  centre  under  the  angle  which 
measures  the  apparent  diameter  of  the  sun,  and  let  us  direct  this 
aperture  toward  the  sun.  It  is  manifest,  according  to  the  law  of 
the  variation  of  calorific  intensity  inversely  as  the  square  of  the 
distance,  that  the  real  action  of  the  sun  on  the  bulb  of  the  thermo- 


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Intelligence  and  Miscellaneoue  AriicUi.  160 

meter  is  identical  with  ihnt  which  would  be  exerted  by  a  disk  of 
8ur&ce  M  placed  at  the  i^perture  (rf  our  sphere,  tius  disk  haying  Uie 
same  tempeniture  and  emissive  power  as  iAie  sun.  We  can  there- 
fore define  the  temperature  of  the  sun  by  that  whidi  would  have  to 
be  attributed  to  this  imaginary  disk,  possessing  the  emissive  power 
of  lamp]i>Uok,  to  produce  upon  the  thermometer  the  same  effect 
which  IS  actually  produced  by  the  sun.  Let  a;  be  t^e  temperature^ 
thus  defined,  of  the  sun,  0  the  stationary  temperature  of  we  ther- 
mometer nceinng  the  solar  radiation  throu^  the  aperture  ta ;  the 
quantity  oi  heat  emitted  by  the  t^rmometer  (which  was  Ba^  at  the 
temperature  t)  has  become  So' ;  and  putting  that  quantity  ot  heat 
equal  to  the  sum  of  the  quantities  enutted  by  enclosure  and  by  the 
sun,  we  have  at  once 

This  is  precisely  the  equation  as  written  by  H.  Yicaire ;  but  it  was 
established  under  reserves  from  which  we  must  now  free  ourselves. 
The  dimensions  of  the  thermometer  are  necessarily  finite ;  and  cof^- 
sequently  the  aperture  thrpugh  which  the  solar  ravs  penetarate  must 
be  widened  to  permit  them  to  reach  the  whole  of  the  bulb :  hence 
comes  a  double  complication. 

Let  us  now  consider  an  admission-aperture  Q  large  enough  for 
an  entire  hemisphere  of  the  bulb  to  receive  the  rays  of  the  sun.  I( 
^e  diameter  of  the  bulb  is  sufiiciently  small  in  proportion  to  that  of 
the  enclosure,  every  point  of  it  will  be  sensibly  in  the  same  condi- 
tions ;  so  that  in  order  to  account  for  the  actual  state  of  the  appa- 
ratus, it  is  sufficient  to  consider  any  one  point  whatever  ox  the 
bulb.  This  point  is  submitted: — (1)  to  the  radiation  of  all  the 
preserved  portion  of  the  enclosure ;  (2)  to  the  radiation  of  the  sun, 
which  is  equivalent  to  that  of  a  surface  w  placed  at  a  distance  equal 
to  the  radius  of  the  enclosure  and  kept  at  the  temperature  of  the 
sun ;  (3)  to  the  radiation  of  the  whole  of  a  portion  of  the  sky  bor- 
dering the  sun,  which  acts  as  ^  surface  Q— im  at  an  unknown  tem- 
perature y.  The  precise  equation  is,  therefore, 
Sa*«  Sa<-f  iMa*-f  Oay. 

I  will  indicate  in  a  forthcomine  note  how,  making  Q  to  vary  by 
means  of  diaphragms  pierced  with  apertures  of  known  dimensions, 
the  correction-term  fl«y  can  be  determined  mth  sufficient  exact- 
ness. An  idea  of  its  quantity  will  be  given  by  the  following  result, 
the  only  one  I  shall  cite  at  present : — 

On  March  14,  1874,  the  sky  being  very  clear,  although  the  ground 
was  covered  with  snow,  at  1  p.m.  the  quantity  of  heat  arriving  from 
the  sun  at  the  surface  of  the  ground  was  the  same  as  that  which 
would  have  been  given  by  a  disk  of  the  same  apparent  diameter  as 
the  sun,  of  maximum  emissive  power,  and  at  the  temperature  of 
1238*^  C.  The  temperature  of  the  air  was  + 1°,  and  the  barometric 
pressure  758  millims.  In  these  conditions,  the  diameter  of  the 
admission-aperture  being  about  25  times  the  sun's  apparent  dia- 
meter, the  portion  of  the  sky  bordering  the  sun,  and  seen  from  the 


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160  Intelligence  and  Miscellaneous  Articles. 

bulb  of  the  thermometer,  acted  as  a  surface  Q  heated  to  near  100^, 
the  enclosure  being  at  9^-2.  The  total  intensities  of  the  three 
radiations  sent  to  the  thermometer  by  the  surfaces  S,  m,  and  O  were 
then  sensibly  proportional  to  the  numbers  15, 1,  and  0*1. 

It  will  not  be  uninteresting,  and  I  have. already  some  measure- 
ments on  this  point,  to  compare  at  different  periods,  and  especially 
at  different  altitudes,  the  radiation  of  this  portion  of  the  sky  bor- 
dering the  sun,  the  illumination  of  which  exhibits  at  times  remark- 
able intensity.  Perhaps  we  shall  find  there  a  portion  of  the  heat 
lost  by  the  direct  rays  in  their  passage  through  our  atmosphere. — 
Oomptes  lUndus  de  VAcad,  des  Scietices,  May  18,  1874. 


ON  A  PECULIAR  PHENOMENON  IN  THE  PATH  OF  THE  ELECTRIC 
SPARK.       BY  PROF.  TOEPLER^  OF  GRA2. 

It  is  well  known  that  the  sparks  from  the  discharge  of  a  Leyden 
jar  leave  upon  the  surfaces  of  insulators  a  trace,  conditioned  by  cer- 
tain mechanical  processes.  The  phenomenon  is  especially  charac- 
teristic upon  very  delicately  smoked  glass  surfaces  to  which  sparks 
spring  between  pointed  conductors.  I  have  therein  observed  a  re- 
gular microscopic  structure. 

With  a  length  of  spark  of  4  to  6  centims.  the  trace  is  generally 
a  bright  streak  3  mlUims.  wide,  with  a  dark  axis,  produced  by  the 
soot-particles  being  partly  throwTi  to  the  sides,  partly  going  to 
the  axis  and  there  accumulating.  On  this  trace  there  is  further 
found  a  mostly  very  striking  knot-like  thickening  just  where  the 
lateral  motion  of  the  air  has  taken  place  with  peculiar  violence — a 
place  in  the  spark  which  had  already  struck  me  in  my  optical 
observations  (Pogg.  Ann,  vol.  cxxxiv.).  Before  this  spot  the 
trace  is  altogether  different  from  what  it  is  beyond.  Towards 
the  positive  conductor  the  spark-path  is  mostly  branched  off  like 
a  tuft,  towards  the  negative  not  so.  When  the  trace  is  ex- 
amined with  a  mcOgnifying-power  of  15-20,  there  appears  fre- 
quently on  the  positive  side,  never  on  the  negative,  in  the  dark 
axis  of  the  spark-path  a  very  fine  dark  zigzag  line  resembliug  a  mi- 
croscopic sine-curve,  of  0- 12-0' 13  millim.  wave-length.  From  the 
internal  angles  of  this  lino  issue  laterally  equidistant  bright  streaks 
inclined  to  the  axis  of  the  spark  in  the  direction  of  motion  of  the 
positive  electricity.  This  microscopic  structure  (the  regularity  of 
which  is  sometimes  surprising)  is  often  found  also  just  as  distinct 
on  the  fine  side  branches  which  break  forth  from  the  positive  part 
of  the  spark-path.  I  remark,  further,  that  the  soot-particles  wnich 
exhibit  the  structure  are  in  some  measure  fixed  to  the  glass  surface ; 
for  when  the  layer  of  soot  is  removed,  say,  with  a  fine  hair  pencil, 
the  dark  streak  in  the  axis  of  the  spark  remains  adhering,  though 
of  course  the  microscopic  delicacy  of  the  figure  is  destroyed. — 
Sitzung  der  math.-naturiv,  Classe  dtr  haiserl,  Akad.  d.  Wissensch,  in 
TTtVn,  May  15,  1874. 


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TH,E 
LONDON,   EDINBURGH,  and  DUBLIN 

PHILOSOPHICAL    MAGAZINE 

AND 

JOURNAL   OF   SCIENCE. 

[FOURTH   SERIES.] 


SEPTEMBER   1874. 


XXVI.  On  the  Opacity  of  the  Developed  Photographic  Image, 
By  Captain  Abnby,  KE.y  F.R.A.8.,  F.C.S.* 

IN  a  series  of  pictures  of  the  sun  which  have  lately  been  taken 
by  photography^  I  found  the  opacity  of  the  image  by  no 
means  varied  directly  as  the  time  of  exposure.  This  caused  me 
to  institute  an  inquiry  into  the  relation  of  time  of  exposure  and 
intensity  of  light  on  the  one  hand,  and  the  resulting  opacity  of 
the  image  on  the  other. 

Primarily  it  was  necessary  to  obtain  some  known  gradation 
of  intensity  of  light,  and  then  to  measure  the  resulting  opacities 
caused  by  it  on  a  photographic  plate.  The  gradation  was  ob- 
tained by  causing  a  "  star  **  to  revolve  rapidly  round  its  centre. 
The  "  star  "  was  cut  out  with  great  exactness  from  white  card- 
board and  made  with  eight ''  points.^'  The  curve  of  each  point  was 
made  to  take  the  form  of  a  portion  of  an  equiangular  spiral. 
By  this  means  an  arithmetical  progression  of  white  was  obtained 
when  the  star  was  made  to  rotate.  When  revolving  in  front 
of  a  black  background,  at  two  inches  from  the  centre  of  the  card 
(and  within  that  distance)  pure  white  was  obtained ;  whilst  at 
fourteen  from  the  centre  pure  black  was  obtained.  The  black 
background  employed  was  of  such  a  dead  nature  that  sunlight 
gave  no  appreciable  shadow  on  it  when  an  opaque  body  was 
placed  before  it. 

The  star  was  made  to  revolve  at  the  rate  of  fifty  revolutions  a 
second.  In  some  cases  a  dead-black  star  was  made  to  rotate 
before  a  clear  sky,  the  only  access  of  light  being  through  the 
openings  of  the  points.  • 

*  Communicated  by  the  Author. 
Phil.  Mag.  S.  4.  Vol.  48.  No.  317.  Sept.  1874.  M 


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162 


Captain  Abney  on  the  Opacity  of  the 


Plated  were  exposed  on  this  object^  the  negatives  being  ob- 
tained by  the  ordinary  wet  process,  with  simply  iodised  collo* 
dion,  an  8-per-cent.  nitrate-of-silver  bath,  and  4-per-cent.  iron 
developer.  The  strength  of  the  developer  was  afterwards  varied ; 
but  for  the  purposes  of  these  experiments  any  variation  was  ex- 
cluded. Other  negatives  were  obtained  on  dry  {Elates  made  with 
bromised  collodion,  a  16-per-cent.  nitrate-of-silver  bath,  albu- 
men preservative  (washed  off,  after  application,  as  far  as  possible), 
and  alkaline  development  of  one  particular  strength.  By  alka- 
line development,  as  is  well  known,  the  bromide  of  silver  is  re- 
duced to  metallic  (or  oxide  of)  silver  in  situ,  no  free  nitrate  of 
silver  being  applied  to  the  image  during  development.  The 
opacity  of  the  image  obtained  by  this  method  is  particularly 
adapted  for  giving  the  necessary  means  of  measuring  the  action 
of  any  relative  intensities  of  light  acting  on  the  silver  for  any  time. 

In  order  to  determine  the  relstive  opacities  of  the  image,  it 
was  necessary  to  obtain  some  standard  scale  with  which  to  mea- 
sure. The  ordinary  methods  were  tried  without  success,  the 
image  being  ''  matt,''  or  only  translucent.  Failure  with  them 
was  inevitable.  After  various  experiments  with  coloured  gela- 
tine wedges,  I  determined  to  use  coloured  glass  wedges,  and, 
owing  to  the  kindness  of  Mr.  Browning,  obtained  three  smoke- 
coloured  ones,  corrected  for  refraction  by  crown  glass.  These 
in  varying  combinations  have  given  me  every  thing  that  could  be 
desired.     The  mounting  I  adopted  for  them  is  as  follows. 

Fig.l. 


U 


A  is  the  wedge  in  position,  B  a  space  in  the  frame  E,  in  which 
any  glass  whose  opacity  is  to  be  measured  is  placed,  C  a  slit, 
and  D  a  fixed  scale  dividing  the  wedge  into  arbitrary  divisions. 
In  actual  use  the  whole  of  the  frame  was  glased  with  finely 
ground  glass,  the  slit  being  next  to  it,  and  the  wedge  against 
that  again.  When  measurements  of  opacity  were  taken,  the 
glass  to  be  tested  was  nlaced  in  B  and  a  light  placed  at  a  known 
distance  behind  the  slit.  Great  care  was  taken  to  ensure  the 
equal  illumination  of  C.  The  length  of  the  wedges  are  severally 
6*5  inches.     They  do  not  give  a  sero  of  absorption  at  their  thin 


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Developed  Photogrtqkhic  Image.  163 

ends^  it  being  found  necessary  in  grinding  to  have  an  appreciable 
thickness.  I  was  enabled  to  calculate  the  relative  absorptive 
values  of  each  wedge ;  and  the  following  Table  will  give  an  idea 
of  the  degree  of  accuracy  with  which  they  were  scaled.  The 
values  are  given  in  lengths  of  a  half-inch  s(»de,  starting  from  the 
calculated  sero  of  the  wedge  which  I  have  called  A.  Each  of 
the  wedges  were  reduced  to  the  same  scale.  The  numbers  refer  to 
different  opacities  which  were  measured.  A  mean  of  six  read- 
ings was  taken  in  each  case ;  and  in  no  instance  did  any  reading 
vary  more  than  '15  from  the  mean. 


A. 

B. 

C. 

No.  I.    . 

.     715 

718 

718 

No.  II.  . 

.  10-21 

10-20 

1018 

No.  III. . 

.  12-44 

12-45 

12-41 

No.  IV.  . 

.  17-60 

17-50 

17-52 

No.  V.   . 

.  18-60 

18-52 

18-52 

From  careful  measurements  it  was  found  that  the  coefficient 
of  absorption  for  each  unit  of  scale  of  wedge  A  for  the  light  with 
which  the  measurements  were  taken  was  *192. 

The  photographs  of  the  rotating  star  were  taken  of  the  full 
size  of  the  original,  only  half  of  the  disk  being  in  some  cases  on 
one  plate.  Strips  were  cut  from  these  negatives,  one  edge 
always  passing  through  the  centre  of  the  image  of  the  star.  The 
relative  transparencies  of  every  \"  or  ^"  were  obtained  by  •com- 
parison with  the  wedges.  From  these  values  the  accompanying 
curves  (fig.  2)  have  been  formed,  the  ordinate  being  the  translu- 
cenc^,  whilst  the  abscissa  is  a  measure  of  the  intensity  of  the 
original  reflected  light.  Only  four  results  are  shown — ^two  ob- 
tained by  wet,  and  two  by  dry  plates.  About  thirty  were 
measured  with  almost  identical  results. 

Each  strip  was  compared  with  the  wedge  by  daylight^  and 
also  by  an  artificial  monochromatic  light.  The  results  obtained 
by  the  one  were  nearly  proportional  to  those  obtained  by  the 
other ;  hence  only  one  curve  for  each  strip  is  given ;  and  this 
was  obtained  by  the  latter  light.  To  guard  against  a  false  ratio 
of  intensity  of  light  due  to  the  lens,  negatives  of  the  star  were 
takmi  at  different  parts  of  the  plate,  and  a  mean  taken.  As  the 
lens  used  was  non-distorting  and  of  long  focus,  the  edge  and 
centre  of  the  plate,  when  directed  towards  the  sky  or  on  a  uni- 
formly white  surface,  had  sensibly  the  same  illumination.  Each 
portion  of  the  strip  cut  from  the  negative  whose  opacity  was 
to  be  compared  was  placed  above  the  wedge,  at  B,  and  opposite 
the  slit  C.  These  were  clamped  together  and  moved  till  Ught 
from  behind,  shining  through  the  slit  and  through  the  image 
and  the  wedge  respectively,  appeared  of  the  same  brightness  on 


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164     On  the  Opacity  of  the  Developed  Photographic  Image. 

the  ground  glass.  The  position  of  the  slit  in  regard  to  the  scale 
was  noted,  and  the  intensity  of  light  transmitted  calculated  by 
the  ordinary  formula.  Each  strip  was  compared  six  times — 
three  times  by  myself^  and  three  times  by  an  assistant.  A  mean 
of  the  six  readings  was  taken  as  correct. 

Fig.  2. 


F C 

A  and  B  tre  the  curves  given  by  the  images  on  the  dry  plates. 

C  and  D  are  the  curves  given  by  the  image  on  wet  plates. 

The  dotted  lines  indicate  the  line  whose  ordinates  give  an  arithmetic 
progression  of  transparency,  £  F  being  unity  or  transparency. 

FG  represents  the  length  of  the  strips  examined,  and  therefore  the 
varying  intensity  of  Ught,  F  being  zero  and  G  the  maximum. 

Regarding  the  curves  given  by  the  dry  plates^  if  we  sup- 
pose 'that  varying  intensities  of  light  cause  a  corresponding  re- 
duction of  the  bromide  of  silver  after  development^  it  can  be 
easily  demonstrated  that  the  intensity  of  light  passing  through 
the  image  after  clearing  away  the  unaltered  bromide  would  be 

l'=:n.e-", (a) 

where  n  and  k  are  constants  depending  on  the  thickness  and 
opacity  of  the  bromide  film^  and  I  the  intensity  of  the  light  pro- 
ducing  any  one  part  of  the  image — ^that  is,  on  the  supposition 
that  the  image  is  formed  of  matter  continuous  but  of  varying 
density.  This  is  not  the  case^  but  there  is  an  approximation  to  it. 
Under  the  same  supposition  we  can  assume  that  there  is  a  function 
of  time  into  a  function  of  intensity  of  light  acting  on  an  infi- 
nitely thin  layer  of  the  bromide  of  silver  which  will  cause  an 
entire  reduction  of  the  bromide  on  development :  this  we  might 
call  a  state  of  saturation.  In  the  image  of  the  star  there  may 
be  some  point  where  the  upper  layer  of  bromide  (of  infinite 
thinness)  is  saturated.  From  that  point  along  the  image  to  be 
produced  bv  the  higher  intensities  the  whole  surface  is  satu- 
rated^ and  the  saturation  must  gradually  approach  the  bottom 
surface.  From  the  point  where  the  whole  depth  of  the  layer  is 
saturated^  along  the  image  to  be  produced  by  still  higher  inten- 


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On  the  Behaviour  of  certain  Fluorescent  Bodies  in  Castor^oil.    165 

sities,  there  can  be  no  further  change.  Here  it  can  be  demon- 
strated that,  between  the  two  points  above  alluded  to,  the  curve 
should  have  the  form 

V^pl-U-r\ {0) 

where  p,  q,r  vre  constants,  and  I  is  the  original  variable  inten- 
sity  producing  the  image.  From  the  last  point  parallelism 
would  result,  and  y  would  become  a  constant.  Theoretically, 
then,  the  measure  of  the  varying  translucency  would  be  com- 
pounded of  (a),  (fi)f  and  a  straight  line. 

The  curves  shown  above  lead  us  to  suspect  that  this  is  the 
practical  result  of  increase  of  intensity  and  time.  From  other 
experiments,  however,  I  am  inclined  to  think  that  even  where 
there  is  no  saturation  the  relation  between  time  and  inten- 
sity is  not  so  simple  as  has  hitherto  been  imagined.  When 
light  actually  reduces  bromide  without  the  aid  of  a  developer, 
a  compound  curve  somewhat  similar  to  (a)  and  09)  will  result. 
In  collodio-chloride  printing  on  glass  a  like  result  would  oc- 
cur. Presumably  the  same  also  occurs  when  printing  on  albu- 
menized  paper.  The  curves  deduced  by  experiment,  and  also 
from  calculation,  show  the  reason  why  iu  a  negative  the  detail  in 
the  shadows  and  highest  lights  is  more  difficult  to  render 
faithfully  than  in  the  half-tones.  They  may  also  show  why  in 
a  print  the  details  in  the  first-named  portions  is  liable  to  be 
obliterated,  even  should  they  be  well  defined  in  the  negative. 

The  curves  measured  from  the  dry  plates  show  that  bromide 
of  silver  is  less  sensitive  to  low  intensities  of  light  than  is  the 
iodide. 

The  action  of  different  strengths  of  developers  I  propose  to 
treat  of  in  a  separate  communication,  as  also  the  relation  between 
time  of  exposure  and  intensity  of  light. 


XX  VII.  A  Note  on  the  Behaviour  of  certain  Fluorescent  Bodies 
in  Castor-oil.    By  Charles  Horner'^. 

SOME  colouring-matters  derived  from  woods,  not  showing 
any  fluorescence  when  dissolved  in  water,  alkaline  solu- 
tions, alum,  or  alcohol,  are  found  to  exhibit  this  phenomenon  on 
treatment  with  castor-oil ;  whilst  other  substances,  which  fluo- 
resce in  alcohol  &c.,  are  observed  to  show  this  property  with 
augmented  intensity. 

To  obtain  clear  solutions,  the  materials  are  first  boiled  in 
alcohol,  filtered,  evaporated  to  dryness,  and  then  heated  with 
the  oil.  On  transferring  some  of  the  prepared  solution  to  a 
test-tube  and  reheating,  the  fluorescence  disappears  as  the  tem- 

*  Communicated  bv  the  Author. 


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166  Baron  N.  Schilling  on  the  Constant  Currents 

Grature  approaches  the  boiling-pointy  bat  retoms  on  cooling, 
oreover  this  operation  may  be  repeated  without  the  substances 
suffering  decomposition.  Cudbear,  camwood,  logwood,  and  tur- 
meric are  selected  as  illustrations  of  the  properties  citdl. 

Cudbear  yields  a  brilliant  orange  fluorescent  light,  and  is 
idsible  in  diffused  daylight  without  the  agency  of  a  condensing 
lens,  which  is  necessary  to  show  it  in  an  alcoholic  solution. 

Camwood  exhibits  a  powerful  apple-green  fluorescence, 
although  wholly  destitute  of  this  propeorty  in  aqueous  or  alco- 
holic media.  The  spectrum  of  the  fluorescent  light  is  continuous 
from  E  downwards,  interrupted  by  two  narrow  faint  shadings 
situated  at  8|  and  5  of  Sorby's  soede. 

With  regard  to  logwood,  unless  the  castor-oil  solution  be  sa- 
turated, sunlight  and  a  lens  are  requisite  to  bring  out  its  fluo- 
rescent character.  The  colour  very  much  resembles  that  of 
camwood,  but  is  distinguished  by  its  spectrum,  which  is  conti- 
nuous from  b,  but  interrupted  by  two  shadings  at  4^  and  5}. 

Turmeric  is  well  known  to  fluoresce  powerfully  in  alcohol  a 
yellow-green,  and  in  benxole  a  blue-green.  In  castor-oil,  how- 
ever, the  fluorescent  light  is  at  least  three  times  as  bright  as 
in  other  fluids,  and  may  be  described  as  a  vivid  emerald-^reen, 
evident  in  the  dullest  daylight ;  but  if  a  flat  bottle  of  the  solution 
be  placed  on  black  velvet  behind  rather  deep  cobalt-glass  when 
the  sun  is  shining,  the  phenomenon  is  of  a  most  brilliant  descrip- 
tion, and  without  exaggeration  may  be  compared  to  that  pro- 
duced by  the  beautiful  uranium-glass.  The  spectrum  furnished 
by  the  fluorescent  light  is  characterised  by  transmission  of  red 
and  green  rays,  and  blue  to  F,  with  a  faintly  perceptible  shading 
at  the  yellow  end  of  the  green. 

These  facts  therefore  show  that,  in  studying  the  phenomena 
of  fluorescence,  advantage  should  be  taken,  whenever  possible, 
of  this  valuable  solvent  property  of  castor-oil. 


XXVIII.  The  Constant  Currents  in  the  Air  and  in  the  Sea :  an 
Attempt  to  r^er  them  to  a  common  Cause,  By  Baron  N.  Schil- 
ling, Captain  in  the  Imperial  Russian  Navy. 
[Concluded  ftrom  p.  109.] 

AS  we  are  speaking  of  wave-motion,  it  will  not  be  out  of 
place  to  mention  here  a  circumstance  which  will  subse- 
quently be  of  importance  for  our  argument. 

It  is  that  the  theory  of  waves,  which  is  commonly  laid  as  a 
foundation  for  all  tidal  phenomena,  has  called  forth  two  views 
which  cannot  possibly  be  both  together  correct.  In  the  first 
place,  it  is  generally  assumed  that  the  flood  tide  rises  just  as  far 


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in  the  Air  and  in  the  Sea. 


167 


above  the  ordinary  aea-level  aB  the  ebb  sinks  below  it.  Secondly, 
it  is  assumed  that  the  middle  time  between  high  and  low  water 
corresponds  to  the  normal  level.  The  highest  water  is  formed 
by  the  two  cusps  A  and  E  (fig.  8)  of  the  tidal  ellipsoid  APES, 

Fig.  3. 


and  the  lowest  bv  the  circle  P  S,  which  halves  the  surface  of  the 
ellipsoid  at  its  mmor  axis.  The  normal  level  will  therefore,  ae- 
cording  to  the  common  assumption,  be  found  on  the  circles  D  C 
and  i^^  6,  which  run  parallel  with  the  circle  P  S  and  are  distant 
45^  of  arc  both  from  the  points  A  and  E  and  from  the  circle 
PS;  so  that  PF=FE  and  PC=AC;  that  is,  about  three 
hours  after  flood  the  normal  level,  and  three  hours  later  the  ebb 
comes  in.  On  this  assumption,  however,  the  superficial  space 
of  the  surfaces  A  C  D  and  E  F  6  together,  occupied  by  the  flood 
tide,  is  2^  times  as  small  as  the  superficies  of  the  middle  zone 
C  F  O  D,  in  which  the  water  stands  at  the  ordinary  level.  But 
since  the  water  which  forms  the  accumulation  of  the  flood  can 
only  be  derived  from  the  ebb-zone,  it  is  clear  that,  on  this  assump^ 
tion,  the  same  mass  of  water  must  rise  considerably  more  on  the 
smaller  space  than  the  water-surface  sinks  in  the  ebb-zone.  If, 
on  the  other  hand,  we  adhere  to  the  assumption  that  the  water 
rises  as  high  above  the  normal  level  as  it  sinks  below  it,  the  sur^ 
face  occupied  by  the  two  floods  must  be  just  as  great  as  that 
occupied  oy  the  middle  ebb-zone,  and  the  two  circles  at  which 
the  normal  level  is  found  must  be  only  30^  distant  from  the 
central  circle,  but  60°  from  the  cusps  A  and  E  of  the  ellipsoid. 
Flood  tide  would  thus  last  eight  hours,  but  ebb  only  four.  Or 
the  water  must  fall  as  much  in  the  last  two  hours  of  its  going 
down  as  in  the  first  four  after  high  water,  and  likewise  rise  as 
much  in  the  first  two  hours  after  its  lowest  as  in  the  remaining 
four.  Probably  the  reality  lies  between  the  two  assumptions ; 
that  is^  the  rise  of  the  water  during  flood  is  probably  more  con- 
siderable than  its  fall  during  ebb,  and,  on  the  other  hand,  the 


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168  Baron  N.  Schilling  on  the  Constant  Currents 

circles  of  normal  level  are  more  than  45^  and  leas  than  SOP  of 
arc  distant  from  the  cusps  of  the  tidal  ellipsoid 'I'. 

As  at  coasts  the  currents  produced  by  the  flow  and  ebb  are 
always  observed  to  flow  alternately  in  precisely  opposite  direc^ 
tions,  it  is  generally  believed  that  the  attraction  of  the  moon  and 
sun  cannot  exert  any  influence  on  the  constant  currents.  Miihry 
says,  *'  It  is  scarcely  necessary  to  mention  that  the  tidal  motion, 
which  daily  carries  its  two  meridian  waves  round  the  globe,  is 
something  altogether  different  from  the  rotation-current:  the 
former  extends  over  all  latitudes,  and  generally  occasions  no 
forward  motion  of  the  mass  of  water,  but  only  waves,  t.  e.  oscil- 
lations ....  Such  an  assumption  is  contradicted  also  in  a  pe- 
culiarly decided  manner  by  the  return*  currents  flowing  on  both 
sides  of  the  equatorial  current  in  a  wide  semicircle  from  west  to 
east  (therefore  against  the  tide-wave) — the  compensation-arms 
of  the  rotation-current,  which  at  the  same  time  enclose  each  a 
wide  central  space  filled  with  still  water  and  floating  seaweed, 
the  Sargasso-seas.  How  can  the  tide-wave  call  forth  such  phe- 
nomena ?  We  are  of  opinion,  moreover,  that,  if  there  were  no 
moon,  the  equatorial  current  would  still  exist  while  the  earth 
revolved  on  its  axis ;  but  it  would  not  exist  if  the  globe  did  not 
turn  on  its  axis,  even  though  the  moon  should  daily  travel  round 
the  earth^t. 

We  cannot  possibly  share  this  opinion  of  Miihry^s.  We  will 
besides  let  the  thing  speak  for  itself,  subjecting  the  action  of  the 
attraction  of  the  sun  and  moon  to  a  closer  consideration. 

Suppose  the  circle  AGED  (fig.  4)  to  be  the  equator,  and 
L  the  centre  of  the  moon,  which  we  will  imagine  in  the  plane  of 
the  equator.  If,  then,  the  earth  had  no  rotation,  the  surface  of 
the  sea  must  take  the  form  of  the  dotted  line  aced.  To  form 
this  ellipsoid,  currents  must  proceed  from  all  sides  towards  the 
cusps  a  and  e,  lasting  until  the  ellipsoid  had  attained  its  due 
elongation.  But  since  the  earth  is  constantly  turning,  the  moon 
relatively  to  the  earth  will  have  already  arrived  at  another  point 
before  the  water  and  the  atmosphere  have  had  time  to  properly 
form  the  ellipsoid  aced.  Of  course  the  currents  will  immedi- 
diately  direct  their  course  to  the  new  point  of  attraction ;  and 
since  this  again  alters  its  position,  a  current  must  be  produced 
in  the  air  and  water  which  must  endeavour  to  follow  the  motion 
of  the  moon  and  shift  the  cusps  of  the  ellipsoid  perpetually  from 
east  to  west.     On  the  other  hand,  by  the  shifting  of  the  moon 


*  It  appears,  therefore,  that  the  zero-point  of  the  tide-gauffes  has  not 
et  received  its  true  position.  This  must  lead  to  erroneous  resulti  in  lerel- 
Jng-surveys  Tvhen  the  heights  of  two  neighbouring  seas  are  to  he  compared 
in  which  the  heiehts  of  the  tides  differ  (as,  for  instance,  Panama). 

t  Miihry,  Veber  die  Lehre  von  den  MeereS'Strommnffen,  p.  9. 


hi 


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in  the  Air  and  m  the  Sea. 


169 


from  L  to  I/,  all  the  points  in  the  titeecaf  are  moved  somewhat 
nearer  to  the  moon,  and  therefore  the  attraction  of  the  moon  on 


Fig.  4. 

A 

<fi- 

^^^ 

{- 

iT^^ 

'-^—-^^ 

\ 

it^^-^:C^ 

--"^ 

\ 

^=^=== 

^"^-"^^^--r^ 

^^,_^ 

all  these  points  is  increased;  while  every  point  in  the  fitc  e^da 
has  removed  a  little  further  from  the  moon,  and  is  consequently 
less  attracted.  We  will  represent  the  attraction  of  the  moon  by 
two  threads  L  c  and  L  d  fastened  to  the  circle.  We  will  gradu- 
ally more  and  more  draw  the  thread  L  c,  to  represent  the  con- 
stantly augmenting  attraction  of  the  point  c.  We  will  constantly 
let  the  thread  L  d  give  way,  to  imitate  the  diminution  of  the 
attraction  of  the  point  d.  Of  course,  through  greater  tension  of 
the  thread  Lc  and  continual  yielding  of  the  thread  LJ,  the 
points  c  and  d  receive  a  motion  in  the  direction  of  the  arrows  C 
and  D.  This  motion  will  be  the  quicker  the  greater  the  circle 
to  which  the  points  belong,  because  in  greater  circles  the  change 
of  distance  from  the  moon,  and  consequently  the  alteration  of 
her  attraction,  is  more  considerable  for  every  point  than  in 
smaller  circles. 

All  that  we  have  just  said  of  the  moon  holds  good  also  for  the 
sun,  with  onl^  this  difference — that  the  motions  of  air  and  water 
produced  by  its  attraction  will  be  somewhat  less  than  those  pro- 
duced by  the  moon. 

We  see  therefore  that  the  attractions  of  the  sun  and  moon 
must  each  present  two  reciprocally  counteracting  developments 
of  force.  The  one,  which  cidls  forth  an  east-to-west  current  and 
corresponds  to  high  water,  we  will  henceforth  name  the  flood- 
current  force ;  the  other,  corresponding  to  the  ebb  and  impelling 
air  and  water  from  west  to  east,  we  will  call  the  ebb-current 
force. 

If  these  two  forces  are  of  equal  intensity,  they  will  balance 
each  other  and  produce  no  current ;  but  as  soon  as  one  of  the 
two  is  greater,  the  water  and  air  will  be  subject  to  the  action  of 
the  greater  force  and  move  onward  with  the  velocity  correspond- 
ing to  the  difference  between  the  two  forces. 


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170  Baron  N.  Schilling  on  the  Constant  Currents 

Before  we  compare^  howeverj  with  one  another  the  quantities 
of  these  two  forces,  it  will  be  necessary  to  illustrate  further  what 
has  been  said,  representing  the  earth  in  the  plane  of  the  meridian. 

Let  the  circle  P  A  S  £  (fig.  5)  be  a  terrestrial  meridian,  and 

Fig.  6. 


L  the  centre  of  the  moon  (or  of  the  sun),  which,  as  before,  is  on 
the  equator.  The  dotted  Wnepase  marks  the  form  of  the  tidal 
ellipsoid.  Through  the  rotation  of  the  earth  the  moon  appa- 
rently moves  from  east  to  west ;  with  it  the  ellipsoid /?  a  s  e  turns 
about  the  axis  P  S,  and  develops,  as  we  have  seen,  at  the  equator 
two  forces  opposed  one  to  the  other.  The  one,  the  force  effect- 
ing the  flood-current,  directs  its  course  from  east  to  west,  and 
in  the  case  here  given  is  strongest  at  the  equator,  on  which  the 
cusps  of  the  ellipsoid  move  forward  as  long  as  the  moon  is  on 
the  equator.  This  force  will  act  in  nearly  the  same  direction  on 
both  sides  of  the  equator;  only  it  must  rapidly  diminish  as  the 
latitude  increases;  and  in  the  latitude  of  the  points  nt,  where 
there  is  no  rise  of  the  water,  the  force  acting  from  east  to  west 
must  be  =0.  Further  polewards  the  tendency  to  form  the 
tidal  ellipsoid  may  probably  develop  an  inconsiaerable  current 
from  the  pole  towards  the  equator,  as  shown  by  the  lines  p  L 
and  s  L. 

The  ebb-current  force  acts  from  west  to  east,  as  if  the  circle 
pCsD  revolved  in  this  direction  on  the  axis  PS.  As  alreadv 
said,  it  arises  from  the  circumstance  that  all  points  in  one  half 
of  the  earth  are  brought  nearer  to  the  moon  by  the  rotation, 
while  all  those  in  the  other  half  are  carried  further  from  it.  The 
ebb-current  force  has  its  greatest  intensity  at  the  equator,  and 
diminishes  very  gradually  on  both  sides  of  it,  since  the  parallel 
circles  in  low  latitudes  become  only  gradually  smaller.  Only  in 
high  latitudes,  where  the  circles  diminish  rapidly,  does  the  force 
of  the  ebb-current  quickly  diminish ;  and  only  at  the  poles  does 
it  entirely  cease. 

Since,  as  we  have  shown,  the  flood  rises  more  above  the  nor- 


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m  the  Air  and  in  the  Sea.  171 

Dial  level  of  the  sea  than  the  ebb  sinks  below  it,  we  think  we 
can  assume,  as  an  hypothesis,  that  the  force  of  the  flood-current 
will  also  be  greater  than  that  of  the  ebb-current. 

In  our  case,  if  the  cusps  of  the  ellipsoid  are  on  the  equator, 
and  therefoie  both  forces  develop  their  maximum  on  that  circle, 
the  greater  force  must  overpower  the  smaller,  and  both  in  air 
and  sea  a  current  from  east  to  west  must  prevail  all  along  the 
equator.  On  both  sides  of  the  equator  the  force  of  the  flood- 
current,  acting  from  east  to  west,  diminishes  rapidly  polewards; 
the  counteracting  force  of  the  ebb-current  diminishes  more 
slowly.  Therefore,  at  a  certain  distance  from  the  equator,  the 
greater  but  rapidly  diminishing  force  directed  from  east  to  west 
will  be  only  just  as  great  as  the  smaller  only  slowly  decreasing 
force  directed  from  west  to  east.  In  these  parallels  the  forces,  ba- 
lancing each  other,  will  generate  no  current.  Still  further  pole- 
wards the  force  of  the  flood*current,  still  continually  more  de- 
creasing, will  be  less  than  that  of  the  ebb-current,  and,  both  in 
the  sea  and  in  the  atmosphere,  currents  from  west  to  east  will 
make  their  appearance.  In  the  latitude  of  the  points  m  the 
east-to-west  force  ceases  entirelv ;  while  the  opposite  force  has 
in  this  latitude  lost  onlv  a  small  portion  (less  than  half)  of  its 
action,  and  hence  mav  here  produce  a  considerable  current.  In 
higher  latitudes  the  force  of  the  ebb-current  will  also  quickly 
diminish,  and  the  currents  from  the  west  become  considerably 
less,  and  their  direction  probably  turn  more  towards  the  equator. 
Accordingly,  in  the  northern  hemisphere,  in  high  latitudes,  cur- 
rents will  arise  from  the  north-west,  and  in  the  southern  from 
the  south-west. 

TVlien,  therefore,  the  moon  and  sun  are  at  the  same  time  in 
the  vicinity  of  the  equator,  a  current  in  air  and  sea  must  flow 
there  from  east  to  west.  On  both  sides  of  the  equator  this  cur- 
rent will  diminish  polewards  until  it  entirely  ceases ;  and  there 
must  thus  be  produced  a  streamless  zone  parallel  to  the  equator. 
Further  polewards  a  west-to-east  current  will  prevail,  which 
must  at  first  increase  gradually  until  it  attains  its  maximum ; 
then  will  this  current  dso  again  diminish  gradually,  and  in  high 
latitudes  flow  from  the  north-west  in  the  northern  hemisphere, 
and  from  the  south-west  in  the  southern. 

In  reality  we  find  this  to  be  the  constitution  of  the  currents. 
In  middle  latitudes  constant  west  winds  and  sea-currents  directed 
eastwards  prevail.  In  the  latitude  of  about  80°  there  is  in  each 
hemisphere  a  zone  of  no  current,  and  in  the  tropical  regions  we 
find  currents  flowing  perpetually  from  east  to  west,  both  in  air 
and  sea.  An  apparent  exception  is,  that  on  the  eouator  we 
meet  with  a  zone  m  which  no  current  is  perceptible  eitner  in  the 
atmosphere  or  in  the  ocean. 


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172  BaroD  N.  Schilling  on  the  Constant  Currents 

This  circamstance  seems  at  the  first  glance  to  contradict  the 
theory  of  the  moon's  attraction;  yet  the  origination  of  this 
equatorial  streamless  zone  is  easily  explained  when  we  reflect 
that  the  moon  and  san  are  simultaneously  in  the  vicinity  of  the 
equator  only  for  a  very  brief  time  twice  yearly.  They  usually 
describe  parallel  circles  which  lie  between  the  equator  and  the 
tropics ;  the  moon  only  goes  sometimes  slightly  beyond  the  last- 
mentioned  circles.  The  ellipsoid  arising  from  the  united  attrac- 
tions of  the  moon  and  sun  must  always  have  its  cusps  between 
the  sun  and  moon ;  and  hence  these  cusps  must  mostly  describe 
parallels  between  the  equator  and  the  tropics. 

Supposing  the  tidal  ellipsoid  in  the  position  asep  (fig.  6), 

Fig.  6. 


its  major  axis  a  e  making  a  certain  angle  with  the  equator 
A  C  E  i)^  by  the  earth's  rotation  on  its  axis  P  S  the  cusps  a 
and  e  of  the  ellipsoid  will  describe  the  parallel  circles  a  a!  ^nd 
eef }  and  therefore  the  maximum  of  the  flood- current  will  also 
be  observed  on  these  parallel  circles.  The  current  will  also  not 
preserve  its  exact  east- to- west  direction^  but^  as  shown  by  the 
arrows  B  and  F^  come  from  E.S.E.  in  the  southern  hemisphere, 
and  from  E.N.E.  in  the  northern. 

On  both  sides  of  the  parallel  circles  a  d  and  e  ff  the  force  of 
the  flood-current  will,  as  already  said,  diminish  rapidly ;  while 
the  ebb-current  keeps,  as  before,  the  maximum  of  its  force  at 
the  greatest  circle,  therefore  at  the  equator,  and,  also  with  this 
position  of  the  ellipsoid,  diminishes  only  slowly  polewards,  con- 


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m  the  Air  and  in  the  Sea.  1 73 

sequently  will  have  already  become  slightly  less  at  the  parallel 
circles  al  a  and  ef  e,  on  which  the  maximum  of  the  flood-carrent 
is  found.  The  direction  of  this  current  will  also  not  be  purely 
from  west  to  east,  but,  as  the  arrows  C  and  D  show,  alternate 
between  W.N.W.  and  W.S.W.  The  opposite  forces  of  the  ebb- 
and  flood-current  mast  therefore  on  both  sides  of  the  parallel 
circles  a  a'  and  e  ef  balance  one  another  and  form  a  zone  of  no 
current. 

This  appears  to  occur  in  the  vicinity  of  the  equator  and  of  the 
parallels  of  30^  latitude,  the  zones  of  calms  and  of  the  Sargasso- 
seas  being  found  there.  In  the  latitudes  of  the  parallel  circles 
a  a' and  ee!  must  be  the  maximum  of  the  east-to-west  flood- 
current  ;  this  perfectly  corresponds  with  the  phenomena  of  the 
trade-winds  and  the  equatorial  currents.  Polewards  from  the 
streamless  zone  in  the  30th  parallel  of  latitude  the  rapidly  dimi- 
nishing force  of  the  flood-current  must  be  overpowered  by  that 
of  the  ebb-current,  and  a  constant  current  from  west  to  east  be 
produced — which  also  actuaUy  happens ;  for  between  the  40th 
and  50th  parallels  of  latitude,  or  thereabouts,  both  in  the  air 
and  in  the  water,  in  all  oceans  and  in  both  hemispheres,  a  cur- 
rent directed  eastwards  is  constantly  observed. 

Hence,  it  seems  to  us,  the  action  of  the  attraction  of  the  sun 
and  moon  explains  the  origination  of  the  trade- winds  and  anti- 
trades with  their  zones  of  calms,  and  the  rotation-currents  run- 
ning parallel  with  the  equator,  with  the  Sargasso-seas  and  the 
streamless  equatorial  zone,  considerably  better  than  all  hitherto 
existing  hypotheses. 

If  our  explanation  of  the  trade- winds  and  equatorial  currents 
is  correct,  also  the  position  and  the  breadth  of  the  current-zones 
and  the  strength  of  the  currents  must  themselves  depend  entirely 
on  the  position  of  the  tidal  ellipsoid  or  on  the  position  of  the 
moon  and  sun  with  respect  to  one  another  and  relative  to  the 
earth.  When,  for  instance,  moon  and  sun  are  both  very  near 
the  equator,  the  equatorial  calm-zone  must  be  non-existent,  the 
calms  of  the  tropics  must  approach  towards  the  equator,  and  the 
constant  west  winds  blow  with  greater  force  in  lower  latitudes. 
Whether  all  this  happens  is  unknown  to  us ;  yet  strong  west 
winds  usually  rage  in  Europe  at  the  times  of  the  equinox. 
Just  so,  perhaps,  it  sometimes  happens  that  ships  cross  the  line 
without  calms ;  but  whether  this  chiefly  coincides  with  the  time 
when  the  moon  crosses  the  equator  we  know  not. 

When  moon  and  sun  are  at  the  same  time  in  the  vicinity  of 
the  tropics,  the  current-zones  must  be  displaced  polewards,  and 
the  equatorial  calm-zone  be  especially  broad.  It  is  possible  that 
then  the  ebb-current  may  predominate  in  the  middle  of  the  zone, 
and  that  this  circumstance  accounts  for  the  west-to-east  current 


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174  Baron  N.  Schilling  on  the  Comtani  Currents 

which  flows  in  a  narrow  band  along  the  equator  and  is  named^ 
in  Berghaus's  'Chart  of  the  World/  the  '' equatorial  counter- 
current/'  In  the  air  this  current  does  not  exist.  It  would 
therefore  have  to  be  ascertained  if  this  equatorial  counter-current 
is  a  constant  one  or  is  only  to  be  observed  when  the  moon  ap- 
proaches the  tropics^  and  whether  it  is  not  wanting  when  the  mm 
and  moon  are  simultaneously  in  the  vicinity  of  the  equator. 

The  shifting  of  the  trade-wind  zones  appears  to  be  on  the 
whole  more  considerable  than  that  of  the  sea-currents,  and  seems 
in  many  cases  to  coincide  with  the  change  of  the  seasons  of  the 
year — which,  then,  proves  that  the  sun  by  its  heat  also  exercises 
an  influence  on  the  trade-winds.  This  probably  takes  place 
chiefly  through  the  sun's  action  on  the  aqueous  vapour  in  the 
atmosphere  and  through  other  collateral  circumstances.  The 
main  cause,  however,  of  the  production  of  the  trade-winds  must 
certainly  be  ascribed  to  the  attraction  of  the  moon  and  sun ; 
and  hence  their  position  relatively  to  each  other  must  have  a 
sensible  influence  upon  various  atmospheric  phenomena.  It 
appears,  therefore,  possible  that  the  well-known  old  popular  tra- 
dition of  the  phases  of  the  moon  affecting  the  change  of  the 
weather  may  have  some  foundation ;  only  it  might  be  more  cor- 
rect to  ascribe  this  influence  not  to  the  phases,  but  to  the  dis- 
tance and  declination  of  the  moon,  which  latter,  it  is  true,  stands 
in  a  certain  connexion  with  the  moon's  phases  and  the  sun's 
declination.  At  the  times,  namely,  of  new  and  full  moon  the 
difference  between  the  declination  of  the  moon  and  that  of  the 
sun  is  always  inconsiderable,  although  at  the  time  of  fuU  moon 
the  sun  and  moon  are  in  different  hemispheres  but  at  nearly 
equal  distance  from  the  equator. 

Only  at  the  time  of  the  quadratures  can  the  difference  of  de- 
clination of  the  sun  and  moon  be  considerable ;  at  the  periods  of 
the  equinoxes  and  the  solstices  the  difference  rises  at  the  utmost 
to  near  28^ 

From  the  production  of  currents  by  the  moon's  attraction  not 
only  can  the  sea-currents  parallel  to  the  equator,  but  also  the 
meridional  currents  be  naturally  derived. 

If  the  whole  earth  were  covered  with  water,  the  equatorial 
current  would  flow  round  it  unhindered ;  but  now  the  continents 
stand  as  insuperable  obstacles  in  the  way  of  this  motion.  As, 
however,  the  cause  of  the  flow  is  not  hereby  removed,  the  cur- 
rent in  the  ocean  must  continue  and  cannot  suddenly  cease  on 
impinging  against  the  coast,  but  must  change  its  dire^lion  ac- 
cording to  the  position  of  the  shore.  Thus  we  aae.  in  Ae 
Atlantic  Ocean,  that  the  southern  equatorial  stream  itvides  at 
Cape  St.  Boque  (which  opposes  it  Uke  a  wedge),  and,  following 
the  direction  of  the  coast,  is  turned  aside,  part  to  the  north-west 


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m  the  Air  and  in  the  Sea.  175 

and  part  to  the  sonth-west.  The  north-west  branch  of  this  car- 
rent  unites  in  the  Caribbean  Sea  with  the  northern  equatorial^ 
and  in  this  way  impels  almost  the  whole  of  the  warmed  water  of 
the  surface  of  the  Atlantic  equatorial  zone  into  the  Gulf  of 
Mexico.  The  great  mass  of  this  warmer  and  therefore  lighter 
water  driven  together  by  the  equatorial  current  must,  of  course, 
have  the  tendency  to  spread  over  the  colder  and  heavier  water, 
and  to  flow  off  northward.  Thus  arises,  then,  a  current  of  warm 
water  flowing  out  of  the  Gulf  of  Mexico,  commonly  known  by 
the  name  of  the  Gulf-stream. 

The  motive  force  of  the  Gulf-stream  musttherefoiebe  derived 
partly  from  the  pressure  of  the  equatorial  current,  partly  from 
the  tendency  of  the  warm  water  to  spread  over  the  cold  of  the 
higher  latitudes,  but  partly  also  from  the  attraction  of  the  cur- 
rent, directed  eastward,  of  the  middle  latitudes ;  but  all  these 
causes  spring  directly  from  the  attraction  of  the  sun  and  moon, 
which  thus  must  be  regarded  as  the  prime  motive  force  of  the 
Gulf-stream*. 

The  eastward  current  of  the  middle  latitudes  and  the  north- 
east movement  of  the  entire  northern  portion  of  the  Atlantic 
Ocean  form  the  continuation  of  the  Gulf-stream,  and  hence  are 
often  designated  by  the  same  name — to  which  we  have  no  ob- 
jection, if  it  be  kept  in  view  that  the  prime  cause  of  motion  of 
the  two  last-mentioned  currents  lies  in  the  force  of  the  ebb-cur- 
rent. As  already  said,  in  about  30°  latitude  this  force  com- 
mences to  overpower  the  force  of  the  flood-current,  and  develops 
the  maximum  of  its  effect  somewhere  between  the  40th  and  50th 
degrees  of  latitude ;  farther  polewards  it  diminishes  considerably, 
and  becomes  so  feeble  that  it  is  no  longer  perceived  as  a  current. 
Nevertheless  a  slight  movement  eastwards  appears  to  extend 
considerably  further  towards  the  pole,  and  gradually  to  collect 
the  warmer  water  on  the  coasts  of  England  and  Norway.  This 
warmer  water  is  derived  partly  from  the  Gulf  of  Mexico;  but 
part  of  it  may  have  been  heated  on  the  surface  of  the  ocean  in 
higher  latitudes.  The  ebb-current,  therefore,  collects  the  su- 
perficial warmer  water  in  the  eastern  part  of  the  ocean ;  and  the 
tendency  of  the  warm  water  to  spread  over  the  colder  impels  it 
north-eastward,  and  thus  accounts  for  the  motion  of  the  north- 
ernportion  of  the  Atlantic. 

The  principal  force  of  the -ebb-current,  flowing  eastward,  is 
deflected  south  by  the  coasts  of  Europe,  and,  following  the  coast 
of  Africa,  returns  again  into  the  equatorial  stream.  The  attrac- 
tion of  the  latter  perhaps  forms  the  principal  cause  of  the  south- 

*  Self-evidently  it  is  not  meant  that  the  tan  and  moon's  attraction  heats 
the  water  of  the  Gnlf  of  Mexico ;  bat  it  is  that  which  generates  the  equa- 
torial current  and  thus  odlects  the  warm  water  in  the  gnlf. 


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176  Baron  N.  SchilliDg  cm  the  Constant  Currents 

ward  bead,  but  may  be  assisted  in  some  degree  by  the  tendency 
of  the  particles  to  move  towards  the  equator^  produced  by  the 
rotation  of  the  earth.  Only  a  small  portion  of  the  east-directed 
current  passes  Cape  Finisterre  unhindered,  and  continues  its 
course  in  the  natural  direction  along  the  north  coast  of  Spain 
till  the  coast  of  France  compels  it  to  curve  sharply  to  the  north- 
west and  follow  exactly  the  course  of  the  shore  of  the  Bay  of 
Biscay,  under  the  name  of  the  Rennell  current,  to  be  lost  at  the 
English  coast  in  the  general  north-east  current  of  the  Atlantic. 
The  Rennell  current  shows  distinctly  how  much  power  the 
direction  of  coasts  has  to  determine  that  of  currents,  even  to 
reverse  their  direction. 

A  portion  of  the  South-Atlantic  equatorial  current  turns  to 
the  south-west  from  Cape  St.  Roque,  along  the  coast  of  South 
America.  The  impelling  force  of  this  Brazilian  current  is  the 
same  as  that  of  the  Oulf-stream — partly  the  pressure  of  the 
equatorial^  partly  the  high  temperature  of  the  water  heated  in 
the  Atlantic  Ocean  and  collected  at  the  coast  by  the  equatorial 
current,  and  partly  the  attraction  of  the  eastward-directed  ebb- 
current  fuiibtioning  in  the  middle  latitudes,  into  which  the 
greater  portion  of  the  Brazilian  current  passes  to  form  the  South- 
Atlantic  rotation-current.  This  latter,  after  crossing  the  ocean 
from  west  to  east,  and  having  curved  a  little  to  the  north,  strikes 
upon  the  African  coast,  and  (for  the  same  reasons  as  those  above 
discussed  for  the  northern  hemisphere)  returns  along  it  again 
to  the  equatorial  current,  forming  the  South-Atlantic  Guinea 
current.  The  entire  rotation-current,  then,  is  originated  by  the 
attraction  of  the  moon  and  the  sun,  as  this  by  its  direct  action 
carries  the  water  in  the  equatorial  regions  from  east  to  west,  and 
in  the  middle  latitudes  from  west  to  east,  and  hence  also  gene- 
rates indirectly  the  currents  flowing  in  the  direction  of  the  meri- 
dian (the  Gulf-stream  and  the  North-African  current,  the  Bra- 
zilian and  the  South-Ouinea  currents). 

In  the  entire  southern  hemisphere  all  the  cold  polar  currents 
are  directed  north-east,  which  coincides  perfectly  with  the  action 
of  the  moon's  attraction  in  higher  latituaes.  Only  in  the  north- 
em  hemisphere  the  directions  of  the  cold  polar  currents  contra- 
dict the  laws  of  the  moon's  attraction ;  for  the  Greenland  cur- 
rent and  the  cold  current  of  the  Japanese  sea  have  a  south-west 
direction,  and  not  a  south-east  one,  which  they  should  have  ac- 
cording to  our  considerations.  This,  however,  may  well  have 
its  cause  in  the  action  of  the  ebb-current,  directed  from  west  to 
east,  which  gradually  withdraws  the  warm  northward-flowing 
current  from  the  coast ;  and  this  is  replaced  partly  by  the  cold 
water  of  the  bottom,  but  principally  bv  the  less-salt  and  there- 
fore lighter  water  derived  from  the  melting  of  the  ice.    A  similar 


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in  the  Air  and  in  the  Sea.  177 

phenomeuoQ  is  often  produced  at  coasts  by  the  action  of  the 
wind;  and  those  who  have  sought  a  sea-bath  will  remember 
that  with  a  land-breeze  the  water  is  always  colder  than  with  a 
sea-breeze.  The  former  removes  the  warmed  superficial  water 
from  the  coast^  by  which  the  colder  water  beneath  is  brought  to 
light.  The  sea-breeze^  on  the  contrary^  drives  to  the  shore  the 
water  which  has  been  warmed  on  the  surface  of  the  sea.  WI  at 
the  wind  does  in  this  case  may  well  be  brought  about  in  a 
higher  degree  by  a  permanent  sea-current.  In  the  depths, 
even  in  the  northern  hemisphere,  the  polar  currents  appear  to 
be  directed  to  the  south-east.  This  is  demonstrated  by  the 
many  icebergs  which,  near  Newfoundland,  cut  through  the 
Gulf-stream  in  that  direction.  Dana^s  chart  of  the  isothermal 
lines  of  the  sea-surface  in  the  coldest  month^,  on  which  the  dis- 
tribution of  the  corals  is  given,  permits  us  also  to  draw  a  similar 
conclusion.  The  polar  limit  of  the  coral  zone,  both  in  the 
Atlantic  and  in  the  Pacific,  is  (probably  on  account  of  the  water 
being  too  cold)  about  lOP  nearer  the  equator  on  the  east  side 
than  on  the  west  side  of  the  same  ocean.  It  is  interesting  that, 
according  to  this  chart,  the  northern  boundary  of  the  corals  is 
10  degrees  more  to  the  north  in  the  Pacific  than  in  the  Atlantic 
Ocean.  The  reason  is  probably  to  be  sought  in  the  fact  that  the 
Atlantic  forms  almost  the  only  discharge^  and  the  main  supply, 
of  the  north  polai'  basin. 

The  alternating  warm  and  colder  strips  of  water  in  the  Gulf- 
stream,  as  well  as  in  the  Kurosiwo,  seem  to  us  to  favour  the 
idea  that  the  force  which  carries  away  from  the  coa^t  the  entire 
current  eastwards  is  not  constantly  of  equal  strength,  but,  so  to 
speak,  has  a  reflex  action — which  perfectly  corresponds  with  our 
hypothesis,  according  to  which,  in  the  middle  latitudes,  the  force 
of  the  ebb-current  must  on  the  whole  take  the  upper  hand,  but, 
through  the  westward-directed  force  of  the  flood-current,  may 
be  subject  Co  periodical  interruptions. 

L.  von  Schrenk,  Member  of  the  Academy  of  Sciences  of  St. 
Petersburg,  has  recently,  in  a  very  interesting  work  [StrdmungS' 
Verhalinisse  im  Ochotskischen  und  Japanischen  Meere),  pointed 
out  that  in  the  Yellow,  as  well  as  in  the  Japanese  and  partially 
in  the  Ochotsk  Sea^  the  temperature  of  the  water  is  constantly 
lower  at  the  east  coasts  of  the  continent  and  the  islands  than  at 
the  west  coasts.  We  see  in  this  a  proof  that  in  these  inland  seas 
there  is  the  same  tendency  of  the  water  to  move  eastwards,  and 
that  thereby  the  upper  warmer  water  is  accumulated  at  the  east 
side  of  the  sea  or  at  the  west  coast  of  the  land.  In  the 
White  Sea  also,  and  the  Varanger  Fjord  in  North  Lapland^ 
the  temperature  of  the  water  is  higher  in  the  eastern  parts  than 
*  Stieler'B  Hand-Atlas,  1867,  No.  9,  Cartoo. 

Phil.  Mag.  S.  4.  Vol.  48.  No.  317.  Sept.  1874.  N 


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178  Baron  N.  Schilling  on  the  Constant  Currents 

in  the  western.  As  we  have  already  remarked,  the  warmer 
water  accumulated  on  a  coast  must  flow  away  polewards,  while 
the  cold  water  of  the  west  side  of  the  sea  seeks  to  occupy  the 
space  left  free,  and  so  flows  towards  the  equator.  It  is  also  in- 
teresting that  Schrenk^  has  pointed  out  the  existence  of  strips 
of  cold  water  in  the  warm  current  of  the  Japanese  Sea.  The 
colder  but  very  slightly  less  salt  water  may,  under  some  circum- 
stances,  have  exactly  the  same  specific  gravity  as  the  warm, 
somewhat  salter  water;  and  hence  they  may  flow  a  long  time 
side  by  side  without  mingling.  These  strips  of  colder  water 
have  not  yet  been  demonstrated  in  the  Brazilian  and  Mozam- 
bique currents ;  but  it  is  probable  that  they  are  present  there 
also,  especially  in  the  Brazilian  current,  which  extends  further 
south.  Indeed  it  is  likely  that  these  warm  currents  are  sepa- 
rated from  the  coast  by  colder  water. 

The  Mozambique  current,  it  seems  to  us,  strikingly  corre- 
sponds with  the  theory  of  the  moon's  attraction.  It  has  its 
origin  in  the  equatorial  stream  of  the  Indian  Ocean,  then  foU 
lows  the  east  coast  of  Africa  in  a  south-westerly  direction, 
and,  still  foUowiug  the  coast,  at  the  southern  extremity  of  the 
continent  takes  a  westward  direction,  but  thereby  comes  into 
the  region  of  the  ebb-current  and  at  once,  with  a  remarkably 
sharp  bend,  returns  eastward.  We  can  only  account  for  this 
sudden  flexion  by  the  action  of  the  moon^s  attraction ;  for  it 
is  impossible  to  admit  that  the  aspirating  force  of  the  Indian 
equatorial  stream  can  occasion  this  sudden  bend  in  order  to 
carry  the  Mozambique  current  to  the  shores  of  Australia  and 
New  Zealand.  Moreover  the  depth  to  which  the  constant 
ocean-currents  extend  appears  to  us  to  be  explicable  only  by 
the  attraction  of  the  moon  and  the  sun ;  for  it  acts  on  all 
the  water-particles  as  far  as  the  bottom  of  the  ocean,  if  its 
action  below  is  slightly  less  than  its  action  above.  The  cur- 
rents of  the  remaining  oceans  are  so  perfectly  similar  to  those 
above  discussed,  that  in  describing  them  we  should  have  to 
repeat  nearly  the  same  things.  They  are  all  originated  prin- 
cipally, either  directly  or  indirectly,  by  the  action  of  the  flood- 
and  ebb-currents,  and  hence  can  only  be  satisfactorily  explained 
by  that  action. 

The  currents  of  the  atmosphere  rest  at  all  events  upon  pre- 
cisely the  same  laws  ;  but  air-currents  are  far  more  susceptible 
to  all  possible  collateral  causes  than  ocean-currents,  and  are 
therefore  subject  to  many  other  influences,  amongst  which  dif- 
ference of  temperature  plays  a  certain  part.  Unfortunately  this 
influence  has  hitherto  been  considerably  overrated;  for  polar 
and  antipolar  currents  generated  by  difference  of  temperature 
*  Op.  cit.  p.  66. 


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in  the  Air  and  in  the  Sea.  179 

have  been  regarded  as  the  basis  of  meteorology,  or  as  currents 
on  which  all  the  movements  of  the  air  depend.  To  this  opinion 
we  cannot  assent ;  on  the  contrary,  we  believe  that  in  the  atmo- 
sphere, just  as  in  the  sea,  the  principal  motions  take  place  in 
directions  nearly  parallel  to  the  equator. 

Perhaps,  in  the  future,  with  more  accurate  knowledge  of  the 
action  called  forth  by  the  attractions  of  the  sun  and  moon,  we 
shall  succeed  in  explaining  the  causes  of  rotatory  storms  by  the 
two  opposite  directions  of  the  flood-  and  ebb-current.  May 
not  in  certain  cases,  at  the  time  of  the  quadratures,  the  ebb-cur* 
rent  caused  by  the  moon  meet  at  a  certain  angle  the  flood-cur- 
rent called  forth  by  the  sun  and  thereby  produce  the  rotating 
motion  f  Up  to  the  present  time  the  important  natural  pheno- 
menon of  cyclones  has  by  no  means  been  explained;  for  all 
hitherto-given  explanations  have  been  quite  inadequate. 

As  is  known,  these  storms  always  have  two  motions — one 
rotating,  and  one  progressive.  The  progressive  motion  corre- 
sponds well  with  the  theory  of  the  moon's  attraction ;  for  these 
storms  almost  always  commence  in  low  latitudes,  and,  in  both 
hemidpheres,  the  centre  of  the  storm  moves  westward  in  the 
region  of  the  flood-current,  at  the  same  time  slightly  increasing 
its  distance  from  the  equator  and  thereby  arriving  m  the  calm- 
zone  of  the  tropic.  Here  the  velocity  of  the  progressive  motion 
becomes  cqnsiderably  less,  and  its  course  makes  a  sharp  curve 
eastward,  the  hurricane  passing  into  the  region  of  the  ebb-cur- 
rent; and  now,  in  both  hemispheres,  it  moves  with  great  velo- 
city to  the  east  and  somewhat  polewards.  Therewith  its  dia- 
meter gradually  increases  and  the  circular  motion  diminishes 
until  the  hurricane  is  lost  in  higher  latitudes.  The  usual  dura- 
tion, from  beginning  to  end,  of  the  hurricane  is  about  14  days. 

The  rotating  motion  of  these  storms  is  subject  to  quite  deter- 
minate but  not  yet  discovered  laws.  In  the  northern  hemisphere 
they  rotate  in  the  opposite  direction  to  that  of  the  hands  of  a 
cluck ;  but  in  the  southern  hemisphere  they  go  round  in  the 
same  direction  as  the  latter.  In  other  words,  in  both  hemi- 
spheres the  storm  always  blows  from  the  west  on  the  side  to- 
wards the  equator,  and  from  the  east  on  the  polar  side.  West- 
wards of  the  centre  of  the  hurricane,  the  direction  of  the  storm 
is  always  to  the  equator ;  eastward  of  the  centre,  away  from  the 
equator;  so  that  hurricanes  rotate  in  an  opposite  direction  to 
the  cuiTcnts  of  the  seas.  Ordinary  storms  appear  to  stand  in 
the  closest  connexion  with  cyclones ;  at  least  this  conjecture  is 
corroborated  by  Buys-Ballot's  law,  according  to  which  the  winds 
revolve  about  the  minimum  of  atmospheric  pressure  in  the  same 
direction  as  the  cyclones. 

The  explanation  that  the  rotating  motion  of  cyclones  arises 

N2 


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180      Prof.  Challis  on  the  Hydrodynamical  Theory  of  the 

from  the  rotation  of  the  earth  is  altogether  inadmissible ;  for 
the  hurricane  always  commences  in  very  low  latitudes^  with  a 
diameter  which  seldom  occupies  more  than  2  or  3  degrees  of 
the  meridian.  The  difference  in  magnitude  of  the  parallel 
circles^  however^  i^  so  inconsiderable  that  the  air  streaming  to 
the  centre  can  only  be  deflected  by  the  earth's  rotation  to  an 
angle  of  2  or  3  degrees  from  the  meridional  direction.  As- 
suming that  the  centre  of  the  cyclone  is^  at  the  beginning  of  the 
hurricane,  in  10^  latitude,  that  its  radius  occupies  2  degrees  of 
the  meridian,  and  that  the  air  requires  two  hours  in  order  to 
traverse  this  distance,  and  retains  during  the  whole  time  the 
rotation-velocity  of  the  parallel  circle  which  it  has  left  behind, 
in  this  case  the  air- particles  from  the  12th  degree  of  latitude, 
streaming  to  the  centre  of  the  hurricane,  would  deviate  a  little 
to  the  west  from  the  meridian,  forming  with  it  an  angle  of  2^45'. 
Those  from  the  8th  degree  of  latitude,  streaming  to  the  centre, 
would  deviate  eastwards,  their  direction  forming  with  the  meri- 
dian an  angle  of  2^  21'.  But  this  much  too  small  deviation 
from  the  meridian  cannot  possibly  occasion  the  rapid  whirling 
motion  of  the  storm. 

Not  doubting  that  such  a  theory  of  the  ocean-currents  and 
the  trade-winds,  founded  on  the  attraction  of  the  moon,  may  be 
the  correct  one,  we  nevertheless  acknowledge  how  much  our  view 
needs  to  be  subjected  to  further  elucidation.  Time  must  bring 
a  multitude  of  fresh  observations  before  the  special  authorities 
can  have  spoken  their  last  word  on  this  subject.  To  us,  how- 
ever, it  will  afford  the  fullest  satisfaction  if  we  have  had  the 
good  fortune,  by  the  foregoing  analysis  of  our  views,  to  contri- 
bute, at  least  indirectly,  to  the  advancement  of  this  department 
of  physical  geography,  which  has  hitherto  wanted  a  uniting  fun- 
damental idea. 

XXIX.  The  Hydrodynamical  Theory  of  the  Action  of  a  Galvanic 
Coil  on  an  external  small  Magnet, — Part  I.  By  Professor 
Challis,  M.A.,  F.R.S.* 

1.  rr  HE  mathematical  theories  of  the  physical  forces  which  I 
-L  have  published  from  time  to  time  in  this  Journal  have 
been  made  to  rest  exclusively  on  the  following  hypotheses  : — All 
visible  and  tangible  substances  consist  of  inert  spherical  atoms 
of  constant  magnitude,  and  all  physical  force  is  either  mode  of 
pressure  of  the  aether  on  the  surfaces  of  the  atoms,  or  reaction 
of  the  atoms  at  their  surfaces  due  to  the  constancy  of  their  form 
and  magnitude.  The  sether  is  supposed  to  be  a  continuous 
elastic  substance,  filling  all  space  not  occupied  by  atoms,  of 
•  Communicated  by  the  Author 


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Action  of  a  Galvanic  Coil  on  an  external  small  Moffnet.     181 

perfect  fluidity,  and  of  the  same  density  every  where  when  at 
rest,  and  when  in  motion  varying  in  density  always  and  at  ali 
points  in  exact  proportion  to  variations  of  its  pressure.  Also 
the  size  of  the  atoms  is  supposed  to  be  so  small  that  even  in 
dense  bodies  they  fill  a  very  small  portion  of  a  given  space. 

2.  These  hypotheses,  which  I  have  enunciated  on  several  pre- 
vious occasions,  are  repeated  here  for  the  purpose  of  directing 
attention  to  what  especially  characterizes  them.  They  involve 
no  assertiun  that  is  not  comprehensible  by  the  indications  of  com-- 
mon  sensation  and  eaiperience.  It  is  because  they  possess  this 
character  that  the  physical  theories  I  have  founded  on  them 
differ  from  those  generally  maintained  by  contemporary  physi- 
cists, which  rest  for  the  most  part  on  experimental  data  con- 

ioined  with  arbitrary  hypotheses  not  in  the  same  manner  intel- 
igible.  It  does  not,  however,  follow  from  the  dissimilarity  of 
the  hypotheses  that  the  two  modes  of  philosophizing  are  con- 
tradictory to  each  other.  This  I  think  I  shall  be  able  to  show 
by  pointing  out  the  distinction  between  their  fundamental  prin- 
ciples, and  the  consequent  relation  in  which  they  stand  to  each 
other. 

3.  For  this  purpose  reference  will  be  more  particularly  made  to 
the  physical  theories  of  magnetism  and  galvanism,  as  proposed 
by  Gauss  and  Ampere,  or  illustrated  and  extended  by  other 
physicists  who  have  adopted  their  views.  The  object  of  all  in- 
vestigations of  this  class  is  to  deduce  from  the  results  of  certain 
fundamental  experiments,  by  the  inter\'ention  of  arbitrary  or 
provisional  hypotheses,  mathematical  expressions  of  the  laws  of 
the  phenomena.  Accordingly  natural  philosophy  is  not  thereby 
advanced  beyond  a  stage  analogous  to  that  to  which  physical 
astronomy  was  brought  by  the  results  of  Kepler^s  observations. 
Newton*8  hypothesis  of  a  gravitating /orc^  varying  inversely  as 
the  square  of  the  distance,  and  his  discovery  of  the  mode  of  cal- 
culating its  effects  by  mathematics,  were  steps  necessary  for 
completing  that  science,  inasmuch  as  they  gave  reasons  for 
Kepler^s  laws.  In  the  empirical  theories  I  am  referring  to,  the 
consideration  of  physical  force  is  included,  and  from  certain 
hypothetical  modes  of  action  of  the  forces  mathematical  expres- 
sions of  the  laws  of  the  phenomena  are  deduced.  But  con- 
fessedly the  intrinsic  nature  of  the  forces,  and  the  reasons  for 
the  facts  and  hypotheses  on  which  the  investigations  rest,  ai*e 
left  undetermined. 

4.  The  final  stage  of  physical  investigation  is  reached  when 
explanations  of  phenomena  and  of  their  laws  have  been  given  by 
means  of  mathematical  deductions  from  hypotheses  satisfying 
the  condition  of  being  intelligible  from  sensation  and  experience. 
Till  this  is  done,  we  can  hardly  be  said  to  have  arrived  at  theory 


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182      Prof.  Challis  on  the  Hydrodynamical  Theory  of  tlie 

properly  so  called.  The  antecedent  steps  of  theory  ought,  for 
distinction,  to  be  called  empirical  or  provisional^  as  resting  on 
arbitrary  hypotheses,  and  as  subsidiary  to  true  and  complete 
theory.  True  theory  rests  on  hypotheses  that  are  not  only  com- 
prehensible^  but  also  ultimate  and  necessary — that  is,  such  as  do 
not  admit  of  being  accounted  for  by  any  ulterior  hypotheses. 
This  will  be  proved  to  be  the  specific  quality  of  the  hypotheses 
stated  above  (art.  1),  if  they  should  be  shown  to  be  adequate  to 
the  explanation  of  the  nature,  laws,  and  consequences  of  the 
operation  of  all  the  different  kinds  of  physical  force.  To  de- 
monstrate their  adequacy  for  this  purpose  has  been  the  express 
object  of  the  many  theoretical  researches  I  have  been  occupied 
with  relative  to  the  modus  operandi  of  physical  force  generally. 
This  course  of  philosophy  I  propose  to  call  Newtonian,  its 
*'  foundation  ^'  having  been  indicated  by  Newton  in  the  Third 
Book  of  the  Principia.  (See  the  discussion  of  this  view  in  the 
Philosophical  Magazine  for  October  1863,  p.  280.) 

5.  Having  thus  pointed  out  that  a  distinction  is  to  be  made 
between  empirical  theory  resting  on  arbitrary  hypotheses  and 
ultimate  theory  resting  on  strictly  a  priori  hypotheses,  I  have 
further  to  state  in  what  respect  the  two  kinds  of  theory  may  be 
considered  to  be  related  to  each  other.  Let  it  be  supposed  that  by 
means  of  a  theory  depending  on  certain  ascertained  facts,  and  on 
hypotheses  thereby  suggested,  a  true  mathematical  expression 
of  the  laws  of  the  phenomena  proposed  to  be  accounted  for  has 
been  obtained.  According  to  views  entertained  by  some  theo- 
rists of  the  present  day,  natural  philosophy  consists  in  thus 
arriving  at  phenomenal  laws,  and  there  is  no  occasion  for  any 
further  investigation.  But  the  principles  of  the  philosophy  I 
call  "Newtonian^'  demand  that  the  explanations  of  all  phe- 
nomena and  their  laws  should  be  inferred  by  mathematical  rea- 
soning from  the  before-mentioned  fundamental  hypotheses. 
Now  this  may  be  done  in  two  ways — either  directly,  by  in- 
dependent deductions  from  the  a  priori  hypotheses,  or  inter- 
mediately, by  deducing  from  the  same  hypotheses  explana- 
tions of  the  facts  and  hypotheses  which  form  the  basis  of  a 
true  empirical  theory.  It  is  evident  that  in  either  way  the  phe- 
nomena are  shown  to  be  consequences  of  the  operation  of  intel- 
ligible causes,  and  are  completely  explained.  It  appears  thus 
that  the  empirical  method  is  subsidiary  to  the  h  prioii  method 
whenever  the  explanation  of  phenomena  is  effected  by  the  aid 
and  intervention  of  the  former,  and  that  in  this  respect  the  two 
methods  may  be  mutually  related.  These  remarks  will  receive 
elucidation  in  the  course  of  the  subsequent  discussions. 

6.  I  propose,  in  the  first  instance,  to  give  an  h  priori  expla- 
nation of  the  facts  relating  to  the  action  of  a  large  magnet  on  a 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet,     183 

small  needle  from  whicb^  by  the  intervention  of  certain  arbitraiy 
hypotheses,  Gauss  inferred  the  law  of  the  inverse  square  in  mag- 
netic action.  For  this  purpose  it  will  be  convenient  to  refer  to 
the  detailed  exhibition  of  Gauss's  argument  given  in  the  Astro- 
nomer Royal's  '  Treatise  on  Magnetism '  (Macmillan  and  Co., 
1870).  I  have  already  discussed  this  question  on  hydrodyna- 
mical  principles  in  a  "  Note  on  the  Hydrodynamical  Theory  of 
Magnetism ''  contained  in  the  Philosophical  Magazine  for  July 
1869,  to  which  I  beg  to  refer  for  details  of  the  mathematical 
reasoning  relating  to  the  physical  conditions  of  magnetic  force. 
I  propose  to  reproduce  here  only  so  much  of  that  discussion  as 
may  be  required  for  understanding  the  subsequent  theory  of  the 
action  of  the  galvanic  coil  on  a  small  magnet,  which  is  the  ulti- 
mate object  of  the  present  communication. 

7.  In  the  article  just  referred  to  it  is  assumed  that  in  a  mag- 
netized bar  there  is  a  small  and  regular  increment  of  atomic 
density  from  end  to  end,  like  that  which  must  be  produced  by 
the  action  of  gravity  from  the  top  to  the  bottom  of  a  solid  or 
fluid  mass  resting  ou  a  horizontal  plane.  In  a  ''  New  Discus- 
sion of  the  Hydrodynamical  Theory  of  Magnetism,''  contained 
in  the  Philosophical  Magazine  for  June  1872, 1  have  proved  (in 
arts.  4-9)  that  if  any  body  in  which  such  gradation  of  density 
exists  be  traversed  either  by  a  steady  setherial  stream,  or  by  a 
uniform  series  of  undulations  of  the  sether,  a  secondary  steady 
stream  will  be  produced  by  impulses  continually  given  to  the 
fluid  in  the  direction  from  the  rarer  to  the  denser  parts  of  the 
body,  this  being  the  direction  of  the  contraction  of  channel 
by  the  occupation  of  space  by  the  atoms.  The  application  of 
this  result  forms  an  essential  part  of  the  hydrodynamical  the- 
ories of  electric  and  magnetic  attractions  and  repulsions  which 
I  have  proposed  and  discussed  in  several  previous  communica- 
tions. In  the  case  of  a  magnet^  the  gradation  of  atomic  density^ 
when  once  induced,  subsists  independently  of  the  action  of  an 
external  body,  and  is  consequently  maintained  by  the  intrinsic 
molecular  forces  of  the  magnet  itself.  Accordingly  I  have  as- 
sumed that  whereas  in  general  the  molecular  attractions  acting 
on  a  given  atom  in  equilibrium  counteract  each  other,  as  do 
also  the  molecular  repulsions,  in  the  case  of  a  magnetized  steel 
bar  the  equilibrium  of  the  atom  results  from  an  equality  between 
the  molecular  attraction  towards  the  denser  end  and  the  mole- 
cular repulsion  towards  the  rarer  end.  This,  in  short,  is  con- 
sidered to  be  the  distinctive  property  of  a  substance  suscep- 
tible of  being  magnetized.  Steel  possesses  this  property  in  an 
eminent  degree,  and  can  be  permanently  magnetized.  Soft 
iron  admits  only  of  temporary  magnetization. 

8.  The  magnetic  state  of  a  substance   being   thus  defined^ 


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18i      Prof.  Challis  on  the  Hydrodipiamical  Theory  of  the 

and  its  magnetic  action  being  supposed  to  be  attributable  to 
the  setherial  streams  which^  as  indicated  above^  this  state  ge- 
nerates when  the  substance  is  traversed  either  by  steady  streams 
or  a  uniform  series  of  vibrations^  we  have  next  to  inquire  re- 
specting the  origination  of  these  primary  movements  of  the 
ffither.  I  thought^  at  firsts  they  might  be  due  to  the  sethe- 
rial streams  which  relatively  pass  through  atpmically  constituted 
substances  in  consequence  of  the  earth's  revolution  about  its 
axis  and  motion  in  its  orbit^  and  of  the  motion  of  the  solar 
system  in  space.  But  since  in  that  case  the  primary^  and  by 
consequence  the  secondary^  motions  would  be  subject  to  large 
fluctuations  of  intensity  to  which  there  is  nothing  corresponding 
in  the  phenomena  of  a  magnet^  it  follows  that  the  streams  which 
are  the  exponents  of  magnetism  cannot  be  to  any  sensible 
amount  due  to  the  above-mentioneil  primaries^  and  must  have 
a  different  origin. 

9.  Having  proved^  as  stated  in  art.  7,  that  the  secondary 
streams  might  be  generated  by  a  uniform  series  of  setherial  un- 
dulations^ and  having  repeatedly  maintained  (in  articles  in  the 
Philosophical  Magazine  and  in  my  work  on  the  Principles  of 
Physics)  that  attractions  and  repulsions  may  be  attributed  to 
the  dynamical  action  of  such  undulations  on  the  individual 
atoms  of  bodies,  it  occurred  to  me  that  those  vibratory  motions 
of  the  sether  which  by  their  attractive  effect  maintain  the  regular 
gradation  of  density  might  be  the  primaries  sought  for;  and 
this  supposition  is  in  accordance  with  the  fact  already  adverted 
to,  that  magnetism  pertains  to  the  magnetized  body  apart  from 
any  extraneous  action.  [See^  respecting  '^ Attraction  by  Vibra- 
tions of  the  Alt"  an  article  in  the  Philosophical  Magazine  for 
April  1871.  I  cannot  but  regard  the  results  of  Mr.  Guthrie's 
experiments  as  singularly  confirmatory  of  my  theoretical  anti- 
cipations.] According  to  the  views  I  have  advocated  relative  to 
molecular  forces,  the  maximum  velocity  of  the  attractive  vibra- 
tions would  be  so  much  larger  than  that  of  the  repulsive  vibra- 
tions, that  in  the  present  inquiry  the  latter  may  be  left  out  of 
account.  Also  it  may  be  presumed  that  it  is  because  that 
maximum  velocity  very  much  exceeds  the  rotatory^  orbital,  and 
translatory  motions  of  the  earth,  that  these  motions  have  com- 
paratively no  magnetic  effect. 

10.  Consequently,  if,  for  simplicity,  the  magnet  be  supposed 
to  be  of  a  cylindrical  form,  in  its  interior  an  impulsive  action 
upon  the  sether  is  continually  operating  in  the  directions  parallel 
to  its  axis.  Now  as  the  attractive  action  of  a  series  of  undula- 
tions is  in  the  direction  contrary  to  that  of  propagation,  and  the 
attraction  is  towards  the  denser  end  of  the  magnet,  it  follows 
that  the  direction  of  the  propagation,  which  is  that  of  the  maxi- 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet.     185 

mum  velocity  in  the  condensed  half  of  the  wave,  is  towards  the 
rarer  end.  At  the  same  time,  according  to  the  mathematical 
result  obtained  in  art.  8  of  the  article  in  the  Philosophical  Ma- 
gazine for  June  1872,  the  impulsive  action  on  the  sether,  whether 
the  primary  vibratory  motions  be  backwards  or  forwards,  is 
towards  the  denser  end,  out  of  which  consequently  the  generated 
streams  flow. 

11.  The  next  point  is  to  determine  the  forms  of  the  courses 
of  the  magnetic  streams  generated  under  the  above-described 
circumstances.  To  do  this  it  is  necessary  to  begin  with  admit- 
ting the  truth  of  the  following  general  hydrodynamical  theorem, 
of  which  great  use  will  be  made  in  the  subsequent  investiga- 
tions. [For  proof  of  the  theorem  see  art.  10  of  the  communi- 
cation just  cited.]  It  is  not  possible  that  the  motion  of  an  un- 
limited fluid  mass  can  be  such  as  to  transfer  any  portion  of  the 
fluid  on  one  side  of  an  unlimited  fixed  plane  to  the  other  side 
without  the  transfer  of  an  equal  portion  from  the  latter  to  the 
former.  Thus  the  motion  must  be  circulating  or  reentering  \ 
and  accordingly  a  general  characteristic  of  magnetic  and  gal- 
vanic currents  is  accounted  for  on  the  principles  of  hydrody- 
namics. 

12.  This  being  understood,  the  forms  of  the  magnetic  linen 
of  motion  are  determinable,  at  least  approximately,  by  the  fol- 
lowing argument.  We  have  seen  that  in  consequence  of  the 
regular  gradation  of  the  atomic  density  of  a  cylindrical  magnet, 
and  the  velocities  due  to  the  outstanding  undulations  which  by 
their  attractive  action  maintain  this  state  of  density,  the  fluid  is 
impelled  in  each  transverse  section  at  every  instant  towards  the 
denser  end  of  the  magnet.  These  impulses  operating  against 
the  inertia  of  the  surrounding  mass  of  fluid,  have  the  effect  of 
generating  streams  which,  as  being  due  to  a  steady  action,  are 
steady,  and^  as  fulfilling  the  condition  stated  in  art.  11^  are  ne- 
cessarily circulating.  To  give  a  first  idea  of  the  courses  of  these 
streams,  at  least  in  the  immediate  neighbourhood  of  the  mag- 
net, I  cannot  do  better  than  refer  to  the  figure  in  p.  17  of  the 
Astronomer  RoyaFs  '  Treatise  on  Magnetism,'  the  directions  of 
the  axes  of  the  small  magnets  indicating  (as  will  be  shown  sub- 
sequently) the  directions  of  the  lines  of  motion  at  the  positions 
where  they  are  situated.  An  approximate  analytical  expression 
for  the  forms  of  these  magnetic  curves  is  derivable  from  the  pre- 
sent theory  by  the  following  investigation. 

13.  From  what  is  argued  above,  the  impulses  are  produced 
by  variations  of  pressure  due  to  variations  of  the  square  of  the 
mean  of  the  velocities  within  the  cylinder  estimated  in  directions 
parallel  to  its  axis,  these  variations  being  caused  exclusively  by 
the  mean  contraction  of  channel  resulting  from  the  increasing 


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186      Prof.  Challis  on  the  Hydrodynamical  Theory  of  the 

occupation  of  space  by  tbe  atoms  towards  the  deuser  end.  Now 
we  may  conceive  this  mean  eflFect  to  result  from  the  separate 
effects  of  a  vast  number  of  atoms  contained  within  a  thin  trans- 
verse slice  of  tbe  cylinder,  inasmuch  as  the  individual  motions 
due  to  the  occupation  of  space  by  the  atoms  may  coexist^  and 
the  parts  of  the  motions  resolved  transversely  to  the  axis  will  in 
that  case  destroy  each  other.  Also  it  is  to  be  considered  tliat 
the  motions  of  the  aether  resulting  from  the  mean  of  the  impulses 
must  satify  the  condition  of  circulating. 

14.  This  being  understood,  it  will  be  seen  to  be  allowable 
to  substitute  for  the  impulsive  effect  of  contraction  of  channel 
that  of  a  motion  forward  in  the  same  direction  of  the  aggre- 
gation of  atoms  contained  in  the  above-mentioned  slice,  the 
fluid  being  relatively  at  rest.  For  on  this  supposition  there 
will  be  a  mean  impulse  parallel  to  the  axis  of  the  cylinder^ 
which  will  be  the  sum  of  the  impulses  of  the  individual  atoms 
resolved  in  that  direction,  and  moreover  will  give  rise  to  a 
drwlating  motion.  The  last  assertion  rests  on  Poisson^s  so- 
lution of  the  problem  of  the  simultaneous  motions  of  a  ball-pen- 
dulum and  the  surrounding  fluid,  according  to  which  the  lines 
of  motion  of  the  fluid  are  reentering ;  and  this  being  the  case 
with  respect  to  each  atom,  the  result  of  the  composition  of  all 
the  motions  will  be  circulating  motion.  Now,  assuming  the 
transverse  section  of  the  cylinder  to  be  small,  it  is  evident 
that  the  stream  resulting  from  the  action  of  all  the  atoms  in 
the  slice  will  have  quum  proxime  the  same  form  as  that  pro- 
duced by  a  single  atom  situated  at  the  middle  point  of  the  slice. 
But  by  Poisson's  solution  we  obtain  the  analytical  expression 
of  the  motion  of  the  fluid  in  this  case.  Hence  a  formula  for 
expressing  the  motion  due  to  all  the  atoms  in  a  given  small 
slice  may  be  at  once  inferred. 

15.  Let  A  and  B  be  the  extreme  points  of  the  axis  of  the 
cylinder,  0  its  middle  point,  P  any  extraneous  point  the  coor- 
dinates of  which  reckoned  from  0  along  and  perpendicular  to 
the  axis  are  p  and  g,  and  Q  being  a  point  of  the  axis  distant  by 
X  from  O ;  let  the  straight  line  joining  P  and  Q  make  an  angle  6 
with  the  positive  direction  of  the  axis.  Then  if  PQar,  /a  be 
the  velocity  of  the  atom,  and  a  its  radius,  by  the  above-men- 
tioned solution  the  velocity  at  P  in  the  direction  from  Q  to  P  is 

^  cos  0,  and  that  perpendicular  to  P  Q  tending  in  the  negative 

direction  is  —-g  sin  6.     Hence,  denoting  by  X  and  Y  the  total 

velocities  resolved  along  and  transversely  to  the  axis,  we  have 

^=  ^  cos« tf-  ^sin« tf,    Y=  ^%08  0 sin  0+  ^sintfcos^: 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet.  187 
or,  since  cos  0=^ ,     sin  ^=  -,  and  r^=  [p—xY  +  q^, 

x^aefi  jLPz:?)*±i?!_    Y=:    ^f^'^^Jp-^) 

Hence^  to  calculate  the  total  velocity  at  P  in  the  longitudinal 
and  transverse  directions,  we  have  to  add  the  velocities  due  to 
all  the  slices  of  given  thickness  dx  from  end  to  end  of  the  mag- 
net, or  to  obtain  the  integrals  k^Xdx  and  k^Ydx  from  a?=  —  / 
to  a?=  +  /,  the  length  of  the  magnet  being  21,  and  *  a  constant 
factor.     The  results  will  be  found  to  be 

Longitudinal^  _  k^ut^ f  p-^l P±i__\ 

velocity     J         2     L((j»-/)«  +  ^«)J      ((;?  +  /)*  +  ^«)?  J  ' 

Transverse  \  _  J^f g q  \ 

velocity   /        2     L(g«+(p-/)«)f       (g« +  (;,  +  /)«)* /• 

16.  It  will  now  be  shown  that  these  velocities  are  propor- 
tional to  the  directive  actions  of  the  magnet  in  the  longitudinal 
and  transverse  directions  on  a  small  needle  having  its  centre  at 
P,  and  movable  about  an  axis  perpendicular  to  the  plane  con- 
taining P  and  the  axis  of  the  cylinder.  The  small  magnet  will 
be  supposed  to  be  surrounded  by  magnetic  streams  exactly  like 
those  which,  according  to  the  foregoing  theory,  belong  to  the 
large  magnet,  and  to  be  of  such  small  dimensions  that  the 
streams  from  the  large  magnet  may  be  considered  to  have  the 
same  direction  and  velocity  at  all  the  positions  of  the  atoms  of  the 
other.  To  find  the  action  of  the  large  magnet  on  the  small  one, 
it  is  now  required  to  determine  for  any  point  the  accelerative 
action  of  the  pressure  of  the  fluid  resulting  from  the  coexistence 
of  the  two  sets  of  motion. 

1 7.  It  is  clearly  not  necessary  to  take  account  of  any  force 
acting*  perpendicularly  to  the  plane  passing  through  P  and  the 
axis  of  the  cylinder,  because  all  such  forces  are  equal  and  oppo- 
site on  the  two  sides  of  the  plane.  Let,  therefore,  that  plane 
contain  the  axes  of  a?  and  y,  and  let  u„  t7.  be  velocities,  parallel 
to  the  axes,  due  to  the  large  magnet,  ana  t^  v^  be  those  due  to 
the  small  one.  Then  by  hydrodynamics,  the  motion  being 
steady,  and,  as  vanishing  at  an  infinite  distance,  such  as  makes 
udx+vdy+wdz  an  exact  differential,  we  have 

p=C-i((tt,+«,)«+K4r^«)- 
Let  V,  be  the  velocity  of  the  incident  stream  of  the  large  mag- 
net, and  let  its  direction  make  an  angle  ^^  with  the  axis  of  x. 
Then  Wj=Vi  cos  ^,  and  t?j=Vj  sin  ^,.     Again^  let  the  velocity 


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188      Prof.  Challis  on  the  Hydrodynamical  Theory  of  the 

of  the  small  magnetos  stream  at  the  position  of  any  one  of  its 
atoms  be  V,,  and  be  in  a  direction  making  the  angle  a  with  the 
axis  of  the  magnet,  and  let  this  axis  make  the  angle  6^  with  the 
axis  of  X,     Then  we  have 

UgSsV^cos  (^g—a),     Va=V2  sin  (^g— «). 

Hence,  by  substituting  in  the  above  expression  for  p, 

;,=C«i(VJ  +  2V,V4C0S  (^^-^,  +  a)-hVj). 

The  pressure  /?,  so  far  as  it  depends  on  the  term  VJ,  can  have 
no  effect  in  producing  either  rotation  or  motion  of  translation  of 
the  small  magnet,  because  the  velocities  Vj  are  symmetrical 
both  with  respect  to  its  axis,  and  to  the  transverse  plane  passing 
through  its  centre.  Hence,  omitting  this  term,  we  have,  since 
y^  and  9,  have  been  supposed  constant,  and  0^  is  a  constant 
angle, 

^P      -tr         /zi       /ivrf.VaCOSa      „     .     .^       /j.rf.VflSina 

-  £  =  V,  cos  {0,-0^)  —^ V,  sin  {0,-0^ j—-  i 

SO 

^P      -ir         //J      /jvrf.VoCOsa      ,,     .     .^      yjvrf.Vasina 

-  fy  =  V. COS {0,-0^)  —1^ V, 8.n  {0,-0,)  —^- 

18.  We  may  now  simplify  the  reasoning,  without  loss  of  ge- 
nerality, by  supposing  that  the  axis  of  x  coincides  with  the  axis 

of  the  small  magnet,  or  that  d^=^0.     In  that  case  S .—  ^p  =0, 

ax 

because  by  reason  of  the  symmetry  of  the  motion  the  positive 
values  of        J are  just  counteracted  by  the  negative,  and 

the  same  is  the  case  with  respect  to  the  values  of  — ^  V  — • 

Hence  the  forces  parallel  to  the  axis  of  the  magnet  have  no  ten- 
dency to  produce  motion  of  translation.  Neither  do  they  tend 
to  produce  rotation,  because  corresponding  to  a  force  at  any 
point  on  one  side  of  the  axis  there  is  an  equal  force  at  an  equal 
distance  on  the  other  side,  and  equally  distant  from  the  axis  of 
motion.    We  have  thus  only  to  consider  the  effects  of  the  forces 

-  ^.     Now  the  sum  of  these  forces  is  zero,  because  by  reason 

of  the  symmetry  of  the  motion,  the  sums  of  the  positive  values 

.^.V^cosa      jd.V-sina  .    ,  i  ^    ^i. 

oi ^ and ^ are  respectively  equal  to  the  sums 

of  their  negative  values.     Hence  there  is  no  tendency  to  motion 
of  translation  transversely  to  the  axis.    Also  the  forces  expressed 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet,     189 

by  the  different  values  of  the  first  term  of  the  formula  for r- 

produce  no  motion  of  rotation^  because  they  are  equal  and  in  the 
same  direction  at  equal  distances  from  the  axis  of  rotation  on 
the  same  side^  whether  positive  or  negative^  of  the  axis  of  the 
magnet. 

19.  But  the  forces  expressed  by  the  second  term  of  the  same 
formula  are  at  a  given  distance  from  the  axis  of  motion  equal 
and  in  the  same  direction  at  points  equally  distant  from  the  axis 
of  the  magnet  on  opposite  sides,  and  at  the  same  time  the  direc- 
tions are  opposite  on  the  opposite  sides  of  the  axis  of  motion. 
Accordingly  these  forces  produce  motion  of  rotation,  and  are 
the  only  forces  that  have  this  effect.  Hence  if  x^  be  the  distance 
of  any  atom  from  the  axis  of  rotation,  the  whole  momentum  of 
rotation  is  propoitional  to 

TT    •    zi      ftx?        rf.VflSina 

—  V,  sin  ^1 X  22 .  X. 5 > 

dy 

the  summation  embracing  all  the  atoms  on  one  side  of  the  axis 
of  rotation.  It  is  now  to  be  considered  that  the  accelerative 
action  of  the  fluid  in  steady  motion  on  any  atom  in  any  direction 
has  a  constant  ratio  to  the  accelerative  force  in  the  same  direc- 
tion of  the  fluid  itself  at  the  position  of  the  atom.  [This  pro- 
position is  proved  in  pp.  313-315  of  *  The  Principles  of  Mathe- 
matics and  Physics.']  Hence,  if  H  be  a  constant  factor  having 
a  certain  ratio  to  the  result  of  the  above  summation,  the  directive 
force  of  the  incident  current  will  be 

HVisin^,, 

tending  always  to  place  the  axis  of  the  small  magnet  in  such  a 
position  that  its  proper  current  along  the  axis  and  the  incident 
current  flow  in  the  same  direction,  in  which  case  d|=0. 

20.  *It  follows  from  the  foregoing  argument  that  the  longitu- 
dinal and  transversal  components  of  a  stream  from  a  large  mag- 
net incident  upon  a  small  one  are  proportional  to  the  directive 
forces  of  the  stream  in  th#two  directions,  and  that  consequently 
the  forces  may  be  supposed  to  be  expressed  by  the  formula  for 
the  velocities  obtained  in  art.  15. 

I  take  occasion  here  to  remark  that  the  Astronomer  Royal 
has  deduced  in  the  Philosophical  Transactions  (vol.  clxii.  p.  492) 
expressions  for  the  same  forces  wholly  different  from  those  in 
art.  15,  by  assuming  the  intensity  of  the  magnetism  along  the 
axis  of  a  magnet  to  vary  proportionally  to  the  distance  from  its 
centre,  and  finds  that  they  give  numerical  results  which  do  not 
sufficiently  agree  with  experiment.  According  to  the  theory  I 
am  advocating  that  assumption  is  not  allowable. 


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190      Prof.  Chailis  on  the  Hydrodynamical  Theory  of  the 

21.  I  proceed  now  to  account  by  the  hydrodynamical  theory 
for  the  experimental  facts  on  which  the  Gaussian  argument  for 
the  law  of  the  inverse  square  in  magnetism  rests.  In  one  set 
of  experiments  the  small  magnet  was  placed  so  that  the  prolon- 
gation of  the  axis  of  the  large  magnet  passed  through  its  centre 
and  cut  its  axis  at  right  angles.  Under  these  circumstances  the 
ordinate  ^=0^  so  that  the  transverse  velocity  vanishes^  and  the 
expression  for  the  longitudinal  velocity  becomes 

kfic^f      1 1      \ 

2    \{p-l)^      {p^l)V' 
which,  if  the  ratio  of  I  top  be  small,  is  very  nearly 

In  another  set  of  experiments  the  small  magnet  was  placed 
with  its  axis  pointing  to  the  centre  of  the  large  one  transversely 
to  the  axis;  in  which  case^  since /?=0^  the  transverse  velocity 
again  vanishes^  and^  supposing  the  ratio  of  /  to  g  to  be  small^ 
the  approximate  expression  for  the  longitudinal  velocity  becomes 

Hence  in  both  cases  the  directive  force  varies  inversely  as  the 
cube  of  the  distance  from  the  centre  of  the  large  magnet,  and  at 
equal  distances  is  double  in  the  former  case  to  what  it  is  in  the 
other.  The  two  principal  results  of  the  experiments  having 
been  thus  accounted  for,  the  hydrodynamical  theory  has  effected, 
at  least  to  a  first  approximation,  all  that  may  strictly  be  de- 
manded from  it.  In  order,  however,  to  exhibit  its  applicability 
more  fully,  I  shall  now  employ  it  to  show  why  Gauss's  empirical 
theory  succeeds  in  representing  the  same  facts. 

22.  It  has  been  inferred  from  the  hydrodynamical  theory  that 
the  action  of  the  large  magnet  on  the  small  one  is  simply  directive* 
Hence,  assuming  that  each  magnet  has  near  its  ends  a  positive 
pole  and  a  negative  pole,  and  that  like  poles  repel  each  other 
and  unlike  poles  mutually  attract,  it  will  readily  be  seen  that, 
according  to  the  arrangements  of  the  two  experiments  described 
in  art.  21,  the  actions  on  the  poles  of  the  small  magnet  are  nearly 
equal,  and  nearly  in  the  same  direction,  and  that  the  action  on 
one  is  attractive  and  that  on  the  other  repulsive.  These  forces 
are,  therefore,  proper  for  acting  as  a  kind  of  cotgple,  and  giving 
direction  to  the  axis  of  the  needle.  Also  in  this  mode  of  viewing 
magnetic  action,  if,  as  is  empirically  assumed,  the  force  varies 
inversely  as  some  power  of  the  distance  from  the  pole,  the  law 
of  the  inverse  square  is  alone  applicable,  because  experiment  and 
the  hydrodynamical  theory  concur  in  indicating  that  the  direc- 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet.     191 

tive  force  varies  nearly  as  the  inverse  cube  of  the  distance  from 
the  centre  of  the  magnet^  which  law  results  from  the  joint  action 
of  an  attractive  and  a  repulsive  force  expressed  thus. 


{r-\-Br)'* 

9    ^ 

the  differential  force  being  nearly  -^— ,  which  for  a  given  value 

of  Br  varies  inversely  as  the  cube  of  the  distance. 

23.  The  whole  preceding  argument  points  to  the  conclusion 
that  the  assumed  attractive  and  repulsive  magnetic  forces  have 
only  a  hypothetical  existence,  and  that  what  really  exists  is  hy- 
drodynamical  pressure. 

24.  Proceeding  now  to  discuss  in  a  similar  manner  the  pro- 
blem of  the  action  of  a  galvanic  coil  on  a  small  magnet,  I  propose, 
first,  to  solve  it  according  to  the  principles  of  the  hydrodyna- 
mical  theory  of  galvanism,  and  then  to  inquire  how  far  the  same 
theory  will  account  for  the  facts  and  hypotheses  on  which  Am- 
pere's empirical  solution  of  the  problem  rests.  The  hydrodyna- 
mical  considerations  will  differ  in  some  essential  respects  from 
those  applicable  to  magnetism. 

25.  First  it  will  be  necessary  to  ascertain  what  motions  of  the 
fiether  correspond  to  the  transmission  of  a  galvanic  current  along 
a  fine  wire.  For  this  purpose  certain  hydrodynamical  theorems 
will  be  employed,  the  principles  and  the  proofs  of  which  I  have 
discussed  in  various  antecedent  researches.  I  consider  it  to  be 
an  axiom  that^  whatever  be  the  motion  of  a  fluid  mass,  the  lines 
of  direction  of  the  motion  may  at  all  times  be  cut  by  a  surface 
made  up  of  portions,  either  finite  or  indefinitely  small,  of  differ- 
ent surfaces  of  continuous  curvature,  so  joined  together  that  the 
tangent  planes  at  the  points  of  junction  of  two  contiguous  por- 
tions do  not  make  a  finite  angle  with  each  other.  The  reason 
for  the  latter  condition  is  a  dyrmmical  one,  whereby  infinite  forces 
are  excluded.  The  other  is  an  abstract  geometrical  condition  of 
continuity,  to  which  the  directions  of  the  motion  of  a  fluid 
assumed  to  be  continuous  are  necessarily  subject,  and  in  virtue  of 
which  the  motion  admits  of  being  calculated.  If  any  one  thinks 
that  there  are  motions  of  a  fluid  which  this  condition  does  not 
embrace,  let  him  calculate  them  if  he  can ;  I  do  not  concern 
myself  with  them. 

26.  It  follows  from  the  foregoing  theorem  that  the  general 
differential  equation  of  the  above-defined  surfaces  of  displacement 
is  (according  to  the  usual  notation)  udX'\-vdy-\-wdz^O,  and 
that  consequently  the  left-hand  side  of  this  equality  is  either  in- 
tegrable  of  itself  or  by  a  factor.  Reasoning  on  the  principle 
that  this  must  be  the  case  always  and  at  ail  points  of  the  fluid. 


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192       Prof.  Challis  on  the  Hydrodynamical  Theory  of  the 

I  have  obtained  a  general  hydiodyuamical  equation  in  which  the 
factor  enters  as  an  unknown  quantity.  The  present  investiga- 
tion does  not  require  reference  to  that  equation  further  than  to 
state  that  it  serves  to  demonstrate  the  reality  of  the  factor^  and 
consequently  to  establish  the  truth  of  the  equation 

/dv      dw\  ,     fdw      du\  .      rdu      dv\     ^  ,  . 

which^  as  is  known^  is  the  general  expression  of  the  condition  that 
udx  4-  vdy  +  wdz  is  integrable  by  a  factor. 

27.  I  have  recently  learnt  with  some  surprise  from  more  than 
one  quarter  that  the  equation  (a),  and^  by  consequence^  the  an- 
tecedent views  on  which  it  is  founded,  are  considered  to  be  untrue 
for  reasons  drawn  from  a  discussion  on  certain  hydrodynamical 
questions  which  I  had  with  Professor  Stokes  in  the  Philoso-* 
phical  Magazine  so  long  ago  as  1842.  Claiming  to  adopt  views 
expressed  by  Professor  Stokes  on  that  occasion,  a  correspondent 
sends  me  the  following  argument  relative  to  the  equation  [a). 
Conceive  to  be  impressed  on  all  parts  of  the  fluid  the  arbitrary 
constant  velocities  a,  ^,  7  in  the  directions  of  the  axes  of  coor- 
dinates.    Then  the  equation  becomes 

,     .    .fio      dw\  .  ,       as  fdw      du\      .     .     .fdu      dv\     ^ 

which,  since  a,  ff,  7  are  perfectly  arbitrary,  cannot  be  true  unless 

dv      ^^_n     ^^      ^"  ~n      ^"     ^^  —A. 
dz      dy^"'     dx       dz  '^   ^     dy      dx~    ^ 

that  is;  unless  in  every  instance  of  the  motion  of  a  fluid 
udx^vdy-\-wdz  is  an  exact  differential.  As  this  is  certainly  not 
the  case,  it  is  concluded  that  the  equation  (a)  is  untrue. 

28.  The  answer  to  this  argument  is  that  the  equation  (a)  was 
deduced  on  the  principle  of  its  being  exclusively  applicable  to  mo- 
tions which  are  peculiar  to  a  fluid,  and  which,  consequently,  a 
solid  is  not  capable  of,  the  motions,  namely,  by  which  the  parts 
of  a  fluid  mass  in  motion  can  change  their  relative  positions. 
This  is  the  sole  raison  d'etre  of  the  equation.  Hence  the  intro- 
duction of  the  velocities  a,  jS,  y  common  to  all  the  parts  of  the 
fluid  is  a  violation  of  the  principle  on  which  it  is  founded ;  or 
rather  the  above  argument  is  a  proof  h  posteriori  that  the  equa- 
tion excludes  such  common  velocities.  If,  therefore,  that  equation 
be  satisfied,  there  is  no  need  to  '^  define  ^'  the  velocity  that  may 
be  common  to  all  the  parts  of  the  fluid ;  for  either  such  motion 
takes  place  under  given  conditions,  and  is  consequently  known, 
or,  if  not  known  and  not  knowable  (whether  it  be  due  to  the 
earth^s  rotatory  and  orbital  motions^  or  to  the  motion  of  the 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet,      193 

solar  system  in  space)  ^  the  determination  of  the  motions  whereby 
the  individual  parts  of  the  fluid  alter  their  relative  positions 
remains  the  same. 

29.  If  while  such  change  of  relative  position  is  taking  place 
each  rectangular  fluid  element  is  also  changing  form^  the  lines 
of  motion  are  necessarily  not  parallel ;  an(i  since^  by  hypothesis^ 
they  are  in  the  directions  of  normals  to  continuous  curved  sur- 
faces, it  follows  that  for  such  motions  v>dx-\-vdy  +  wdz  is  an  exact 
difierential.  But  if  each  rectangular  element  retains  the  same 
form^  the  lines  of  motion  must  be  parallel^  the  surfaces  of  dis- 
placement are  planes,  and  udx+vdy-k-wdz  is  integrable  by  a 
factor. 

In  the  course  of  my  many  hydrodynamical  researches  I  have 
had  from  time  to  time  the  benefit  of  criticisms^  and  arguments 
ex  adverso,  from  my  mathematical  contemporaries ;  and  I  wil- 
lingly admit  that  I  have  thereby  been  induced  in  several  instances 
to  modify  my  original  views.  But  hitherto  I  have  not  perceived 
that  there  is  any  ground  for  questioning  the  truth  of  the  prin- 
ciples and  the  reasoning  which  have  conducted  me  to  the  equation 
which  I  call  the  third  general  equation  of  hydrodynamics,  and  I 
have  consequently  not  hesitated  to  employ  the  equation  (a), 
which  is  a  logical  consequence  of  that  general  equation,  in  lay- 
ing a  foundation  for  the  subjoined  hydrodynamical  theory  of  the 
action  of  a  galvanic  coil. 

30.  A  current  of  the  sether  being  supposed  to  flow  uniformly 
along  a  straight  cylindrical  conductor,  the  motion  of  the  fluid 
at  any  point  may  be  determined  by  the  following  reasoning 
(given  in  more  detail  in  the  '  Principles  of  Physics,'  pp.  563-565) . 
The  motion  is  plainly  a  function  of  the  distance  from  the  axis  of 
the  cylinder,  but  cannot  be  wholly  parallel  to  it ;  for  if  that  were 
the  case,  since  the  motion  is,  by  hypothesis,  steady,  and  in  such 
motion  the  pressure  is  everywhere  less  as  the  velocity  is  greater, 
and  sinc«  in  this  instance  the  velocity  will  evidently  be  less  the 
greater  the  distance  from  the  axis,  it  would  follow  that  on  all 
sides  there  would  be  tendency  to  motion  towards  the  axis,  which, 
if  not  counteracted,  would  put  a  stop  to  the  current.  To  coun-. 
teract  this  tendency  there  must  be  centrifugal  force  due  to  cir- 
cular motion  about  the  axis ;  and  according  to  the  hydrodyna- 
mics of  steady  motion  the  rectilinear  and  circular  motions  may 
coexist.  Hence,  if  r  be  the  distance  from  the  axis,  and  the  rec- 
tilinear and  circular  motions  at  that  distance  be  respectively 
F(r)  and/(r),  we  shall  have 

u=^f[r),    t.=  -^y(r),     w=¥{r). 

These  equations  satisfy  the  condition  of  constancy  of  mass  ex- 
Phil.  Mag.  S.  4.  Vol.  48.  No.  317.  Sept.  1874.  O 


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194       Prof.  Challis  on  the  Hydrodynamical  Theory  of  the 
pressed  by  the  equation 

dx      dy      dz^  * 

which  is  true  for  a  compressible  fluid  inclusively  of  small  terms 
of  the  second  order ;  so  that  the  subsequent  reasoning,  although 
strictly  applicable  to  an  incompressible  fluid,  may  be  taken  to 
apply  to  the  sether.      Now,  from  the  known  expressions  for 

^«  -J-}  -^  for  steady  motions  of  an  incompressible  fluid,  it 
will  readily  be  found  that 

W  ^  {My  ^  the  centrifugal  force. 

8L  These  results  are  independent  of  the  forms  of  the  func- 
tions f(r)  and  F(r)  and  of  any  relation  between  them.  But 
since  the  assumed  values  of  u,  v,  w  do  not  make  udx  +  vdy  +  wdz 
an  exact  differential,  according  to  the  principles  maintained  above, 
they  must  be  such  as  to  satisfy  the  equation  (a).  By  substitu- 
ting them  in  that  equation,  and  integrating,  the  result  is 

F(r)  -  r' 

c  being  the  arbitrary  constant  introduced  by  the  integration. 
We  have  thus  demonstrated  that  the  current  must  be  such  as  to 
satisfy  the  relation  between  the  velocities/(r)  and  F(r)  indicated 
by  this  equation. 

32.  By  taking  account  of  this  relation  the  equation 

udx + vdy '^  wdz =0 
gives 

^^  "  rW)  ^^^^^y^  ^  ^  (xdy-ydx). 
Hence,  by  integration, 

xrssctan"*-  +J, 

X 

which  is  the  general  equation  of  the  surfaces  of  displacement, 
the  orthogonfd  trajectories  of  which  determine  the  directions  of 

the  motion.     If  tan~'-a^,  and  r,  be  a  given  distance  from  the 

axis,  we  have 

which  shows  that  the  motion  in  the  cylindrical  surface  of  radius 
r,  consists  of  spiral  motions  the  directions  of  which  make  with 


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Action  of  a  Oalvcmic  Coil  on  an  external  email  Magnet.     196 

parallels  to  the  axis  the  angle  whose  tangent  is  -^.    The  motion 

is  thus  completely  determined  if  only  the  forms  of  the  functions 
f(r)  and  F(r)  can  be  found.  In  my  work  already  cited  I  have 
expressed  (in  p.  566)  a  doubt  as  to  the  practicability  of  doing 
this  in  the  existing  state  of  hydrodynamics.  I  have/  however, 
since  discovered  the  following  argument,  which  I  consider  to  be 
adequate  to  this  purpose. 

33.  Suppose  the  straight  galvanic  current  to  be  cut  by  a  plane 
transversely,  and  on  the  plane  three  concentric  circles  to  be  de- 
scribed having  the  common  centre  on  the  axis,  and  let  their 
rady  be  r+«,  r,  and  r— «,  «  being  verj'  small.  Also  let  there  be 
drawn  in  the  plane  from  that  centre  two  straight  lines  separated 
by  the  small  angle  80.     Then  the  space  bounded  by  these  lines 

and  the  first  and  second  circles  is  ((r+«)*— ^))-o-#  ^^^  ^^^^ 

bounded  by  the  same  lines  and  the  second  and  third  circles  is 

80 
(r*—  (r— «)*)  -^.  Now,  according  to  the  foregoing  investigation, 

these  spaces  may  be  considered  to  be  transverse  sections  of  ele- 
mentary channels  in  which  the  galvanic  current  is  constrained  to 
move.  Let  V  be  the  mean  velocity  of  the  current  through  the 
space  furthest  from  the  axis,  and  V  that  of  the  current  through 
the  other.    Then,  inclusively  of  small  terms  of  the  second  order, 

V'=F  fr+  ^Yand  V=F(r-  ^Y     Hence  the  excess  of  fluid 

which  in  a  second  of  time  passes  through  the  larger  space  above 
that  which  in  the  same  time  passes  through  the  other  is 

which,  omitting  terms  containing  efi  &c.,  becomes 

34.  We  have  now  to  take  into  account  the  principle  adverted 
to  in  art.  11,  according  to  which  the  inertia  of  an  unlimited  mass 
of  incompressible  fluid  opposes  an  insuperable  obstacle  to  any 
alteration  of  the  quantities  of  the  mass  on  the  two  sides  of  any 
unlimited  fixed  plane.  Since  in  the  case  of  the  galvanic  current 
fluid  is  being  transferred  every  instant  across  the  above-men- 
tioned transverse  plane,  not  only  roust  the  rheophore  furnish  a 
channel  for  the  circulation  of  the  fluid,  but  there  must  also  be  a 
general  stress,  like  hydrostatic  pressure,  which,  taking  effect 
always  in  the  directions  of  any  channels  of  circulation,  maintains 

02 


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196       Prof.  Challis  on  the  Hydrodynamical  Theory  of  the 

the  current  in  opposition  to  the  tendency  of  the  inertia  of  the 
fluid  to  put  a  stop  to  it.  In  the  present  theory  this  stress  is  due 
to  the  action  of  the  battery ;  the  wire  supplies  a  channel  for  the 
current;  and^  as  is  shown  in  art.  11^  it  is  dynamically  necessary 
that  the  current  should  flow  in  a  complete  circuit. 

35.  It  is  clearly  possible  that  the  form  of  the  function  F(r) 
might  be  determined  by  arbitrary  conditions.  For  instance^  if 
the  above-mentioned  stress  were  arbitrarily  caused  to  be  the  same 
at  all  points  of  the  transverse  plane^  the  velocity  parallel  to  the 
axis  would  be  the  same  at  all  points^  and  F(r)  would  be  a  constant. 
But  it  is  evident  that  this  is  not  true  of  a  galvanic  current.  The 
principle  of  the  present  inquiry  demands  that  as  a  definite  rela- 
tion between  the  functions  y][r)  and  F(r)  was  obtained  in  a  unique 
manner  by  integration^  the  form  of  the  function  F(r)  should  be 
similarly  determined.  Now  the  only  way  in  which  that  form  can 
be  obtained  exclusively  by  integration  is  to  equate  to  zero  the 

above  factor  — ^  H — ">      >  ^^  which  case  integration  gives 

Thus  the  velocity  parallel  to  the  axis  varies  inversely  as  the  dis- 
tance from  the  axis ;  and  the  stress  which  maintains  that  velocity, 
and  is  therefore  proportional  to  it^  varies  according  to  the  same 
law.  Since  the  transverse  sections  of  the  elementary  channels 
above  defined  vary  directly  as  the  distances^  it  follows  that 
through  each  elementary  channel  outside  the  wire  the  same 
quantity  of  fluid  flows  in  a  given  interval.     Also^  since  it  has 

c 
been  shown  (art.  31)  that/(r)=  -  F(r),  we  obtain 

or  the  transverse  circular  motion  varies  inversely  as  the  square 
of  the  distance.  These  results  are  essential  to  the  hydrodyna- 
mical theory  of  galvanism. 

36.  But  for  the  theory  of  the  action  of  a  galvanic  coil  we  re- 
quire to  know  the  motion  of  an  setherial  current  along  a  fine 
wire  the  axis  of  which  has  the  form  of  a  circle^  and  the  trans- 
verse section  of  which  is  circular  and  uniform.  For  this  case  it 
will  be  assumed  that^  by  reason  of  symmetry^  the  motion  at  any 
given  point  is  compounded  of  motion  parallel  to  the  axis^  and  of 
motion  in  the  plane  passing  through  the  point  and  the  centre  of 
the  axis^  and  cutting  the  axis  at  right  angles.  Let  the  plane  of 
this  axis  be  parallel  to  that  of  xy,  and  its  centre  be  on  the  axis 
of  z  'i  and  let  h  be  the  height  above  the  plane  xy  of  the  point  of 
intersection  of  the  circular  axis  by  the  above-mentioned  trans- 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet.      197 

verse  plane^  and  a  the  distance  of  the  same  point  from  the  axis 
of  z.  Also  in  the  same  plane  let  r  and  0  be  the  polar  coordi- 
nates of  the  given  point  P  referred  to  the  point  of  intersection 
as  pole^  and  to  the  straight  line  through  the  pole  parallel  to  the 
plane  xy.  Then,  the  rectangular  coordinates  of  P  being  x,  y,  z^ 
if  we  put  R  for  (a?'-f  y')^,  and  suppose  the  velocity  parallel  to 
the  plane  ocy  to  be  F(R,  z),  and  that  in  the  transverse  plane  to 
be  f{r,  0),  we  have 


together  with   the   equalities  r*  =  (z  —  A)*  -f  (R  —  a)*,    and 

z~-k 
tan  tf  =  p .    By  analytical  operations,  the  details  of  which,  as 

being  somewhat  long  but  presenting  no  difficulties,  are  not  in- 
serted here,   it   may   be  shown    (1)    that    7"  + T"  +  ;/~=0# 

(2)  that  udx+vdy-hwdz  is  not  an  exact  differential;  (8)  that  by 
substitution  in  the  equation  {a)  there  results  the  following  equa- 
tion of  condition  connecting  the  functions  /  and  F : 

37.  Respecting  this  equation  we  may,  first,  remark  that  since 

it  does  not  contain  ^  it  shows  that  the  assumed  motion  requires 

that /should  be  a  function  of  r  only,  and  consequently  the  mo- 
tion in  planes  transverse  to  the  axis  of  the  wire  is  proved  to  be 
circular.  This  result  is  in  accordance  with  the  original  assump- 
tion, that  the  transverse  section  of  the  wire  is  circular,  as  should 
plainly  be  the  case,  since  the  surface  of  the  wire  bounds  the  cir- 
cular motion. 

38.  The  proof  that /is  a  function  of  r  only  having  taken  no 
account  of  the  magnitude  of  a,  and  being  clearly  independent  of 
that  of  h,  we  may  infer  that  the  function  has  the  same  form 
whatever  be  the  radius  of  the  axis  of  the  wire,  and  therefore  the 
same  as  if  the  radius  were  infinite,  in  which  case  a  finite  portion 
of  the  wire  might  be  considered  to  be  a  straight  cylinder.     But 

we  have  shown  (art.  35)  that  for  the  straight  cylinder/(^r)  =  4. 

Consequently,  substituting  this  value  of /(r)  in  the  equation  (i), 


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198       Prof.  Challis  on  the  Hydrodynamicd  Theory  of  the 
there  results  for  determining  the  form  of  the  function  F  the 


equation 


-2+W-|J(-*)-v^(«-)=0- 


This  partial  differential  equation  integrated  in  the  usual  way 
gives 


*'"'II(z-A)'*U-a)- 


Now  it  is  certain  that  the  expression  for  the  velocity  F(R,  z) 
must  involve  the  distance  r  of  the  point  P  from  the  axis  of  the 
wire.  This  condition  is  satisfied  by  the  above  value  of  F  by 
assuming  that 


*fe-)-('-f^T' 


and  can  be  satisfied  in  no  other  way.  We  have  therefore  the 
unique  solution 

p_ C, C^ 

R((^»A)«+  (R-fl)«)i      ^ 

C,  being  an  arbitrary  constant.  Thus  exact  expressions  for  the 
velocity  in  any  plane  transverse  to  the  axis  and  for  that  parallel 
to  the  axis  having  been  found,  the  total  motion,  which  is  com- 
posed of  these  two,  is  completdy  determined. 

89.  From  the  above  expression  for  F,  that  which  applies  to  a 
straight  cylindrical  wire  mav  readily  be  deduced.  For  putting 
a  +  «  for  R,  ft  being  a  variable  quantity  restricted  within  compa- 
ratively small  limits,  and  giving  to  C,  the  form  {/a,  </  being  an 
arbitrary  factor,  we  have 

F=      '^'^  ""' 


(fl+«)r 


('-i> 


which  for  a  straight  wire,  for  which  a  is  infinite,  becomes 


r 


agreeing  with  the  result  obtained  in  art.  35. 

40.  It  would  seem  that  the  foregoing  investigation  might  be 
-generalized  so  as  to  apply  to  a  wire  conductor  of  any  form,  when 
it  is  considered  that  the  determinations  in  arts.  30-35  of  the 
forms  of  F(r)  and/(r)  for  a  straight  cylinder  did  not  involve  the 
length  of  the  axis,  and  would  remain  the  same  for  a  cylinder  of 
infiinitesimal  length  if  the  condition  of  circular  motion  about  the 
axis  were  satisfied.  We  have  shown  that  this  condition  is  in  fact 
satisfied  by  a  uniform  conductor  of  circular  form,  which  may  be 
regarded  as  made  up  of  a  series  of  right  cylinders  of  infinitesimal 


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Action  of  a  Galvanic  Coil  on  an  external  small  Magnet.     199 

lengths ;  and  as  any  portion  of  a  uniform  conductor  of  any  form 
may  be  supposed  to  be  similarly  composed^  the  expressions  for 
/(r)  and  F(r)  for  a  circular  wire  would  appear  to  apply  generally^ 
if  the  radius  a  be  taken  to  represent  the  varying  radius  of  curva- 
ture of  the  axis  of  the  wire.  This  question^  however^  requires 
more  consideration  than  I  can  now  give  to  it. 

41.  Returning  now  to  the  circular  conductor^  if  in  the  expres- 
sions for  u,  V,  w  in  art.  36  the  values  found  for  /(r,  6)  and 
F(R,  z)  be  substituted,  we  shall  have 

cjp{z-h)      c^ 

c^yjz'-h)  _  c^ 
^^  R/^  RV 

g|(R-"a) 

Hence,  since  R*=^+y*  and  r*=  (ar— A)«+  (R_fl)«,  it  will  be 
found  that 

^  r        (z— A)*4-(R— «)*         r      x^  +  y^ 

Consequently  the  right-hand  side  of  this  equation  becomes  an 
exact  differential  when  multiplied  by  the  factor  r.  Before  pro- 
ceeding to  the  next  step,  it  is  necessary  to  take  into  account  that 
in  the  foregoing  investigation  the  arbitrary  constants  e,  and  c^ 
have  been  introduced  in  such  manner  as  to  show  that  they 
are  wholly  independent  of  each  other.  Hence,  on  equating 
r{udx+vdy+wdz)  to  zero,  we  must  have  separately 

(z— A)dR  — (R--g)ig  _^  ydx—xdy __^ 

which  means  that  both  the  motion  transverse  to  the  axis  of  the 
wire  and  that  parallel  to  the  same  are  such  as  require  a  factor 
for  making  udx + vdy  +  wdz  integrable.  Both  are  steady  motions 
and  therefore  coexist.  Instead  of  the  above  two  equations  we 
may,  by  introducing  an  arbitrary  constant  factor  X,  employ  the 
single  equation 

(z— A)rfR-  (R,—a)dz  ydx—xdy __^ 

Hence,  by  integration, 

C=c,tan-*^^^+\Cjtan-*^ssCi^H-\c^, 

supposing  that  ^=tan^,  and,  as  before,  that  =-— =  tantf. 


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200         Prof.  A.  Stoletow  on  the  Magnetization- Functions 
DiffereDtiating  this  last  equation^  we  get  0=c  d0+\c^<f>,  or 

dif}'^        c, 

42.  Assuming  that  c^  and  c,  are  positive  quantities  in  the 
expressions  for  u,  v,  w  in  art.  41,  it  will  be  seen  that  those  values 
were  formed  so  that  6  and  <b  each  decrease  with  the  motion. 

Hence  ^will  be  positive,  and  X  must  be  a  negative  quan- 
tity. According  to  the  supposed  directions  of  the  decrements, 
the  spiral  motion  will  be  dextrorsum.  If  the  motion  were 
assumed  to  be  such  that  d0  and  d<f>  had  different  signs,  the 
spiral  motion  would  be  sinistrorsum,  and  we  might  by  the  same 
reasoning  as  before  obtain  C=c^6'\'\^c^<f>,  c^  and  c^  being  still 

positive.     In  that  case  tt  = ^=  a  negative  quantity,  and  V 

is  consequently  positive.  As  the  factors  X  and  X'  are  wholly 
arbitrary,  we  have  thus  shown  that,  as  far  as  hydrodynamics  is 
concerned,  the  galvanic  current  might  be  either  dexirorsum  or 
sinistrorsum. 

Having  in  the  preliminary  part  of  this  communication  dis- 
cussed the  action  of  a  large  magnet  on  a  small  one,  and  having 
now  ascertained  the  exact  form  of  a  galvanic  current  along  a  cir- 
cular wire,  I  propose  in  a  second  Part  to  investigate  the  action 
of  a  galvanic  coil  on  a  small  magnet,  and  to  show  why  it  agrees 
approximately  with  that  of  a  magnet,  and  in  what  respect  espe- 
cially the  two  actions  differ.  In  the  course  of  the  investigation 
the  facts  on  which  Ampere's  theory  rests  will  be  accounted  for 
by  the  hydrodynamical  theory,  for  the  purpose  of  fully  establish- 
ing the  claim  of  the  latter  to  be  considered  a  strictly  h  priori 
theory. 

Cambridge,  August  10,  1874. 


XXX.   On  the  Magnetization-Functions  of  various  Iron  Bodies, 
By  Professor  A.  Stoletow*. 

IN  my  work  on  the  magnetization  of  ironf  I  have  taken 
Neumann's  coefiScient  «  as  a  measure  of  the  magnetizability. 
This,  as  is  well  known,  expresses  the  ratio  in  which  the  magnetic 
moment,  referred  to  the  unit  of  volume,  stands  to  the  quantity 
of  the  magnetizing  force,  presupposing  that  the  iron  forms  an 

*  Translated,  from  a  separate  impression  communicated  by  the  Author, 
from  the  Bulletin  de  la  SocUt4  Imp,  des  Naturalistes  de  Moscou,  1873, 
No.  4. 

t  Pogg.  Ann.  vol.  cxliv.  p.  439;  Phil.  Mag.  S.  4.  vol.  xlv.  p.  40 ;  more 
fully  at  a  separate  brochure  in  Russian,  Moscow,  1872. 


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of  various  Iron  Bodies.  20 1 

nfiaitely  long  cylinder  and  is  uniformly  magnetized  longitadi- 
nally.     I  have  named  this  coefficient  (in  that  essay  denoted  by 
k)  the  magnetizing -function  of  the  given  iron,  since  it  depends 
on  the  quantity  of  the  magnetizing  force.     A.n  analysis,  namely^ 
of  the  experiments  of  Quintus  Icilius  (with  ellipsoids)  and  of 
my  own  (with  a  ring)  showed  that  the  function  k  at  first  in- 
creases rapidly  as  the  decomposing  force  rises^  and  then  again 
diminishes.     This  behavour  seems  to  take  place  with  all  sorts  of 
iron ;  yet  the  absolute  numerical  values  of  ky  with  the  same  val  ue 
of  the  argument,  are  very  different,  according  to  the  quality  of 
the  iron.     These  results  have  been  corroborated  by  a  thoroug  h 
investigation   by  Mr.  H.  A.  Rowland*.     He  shows  that    the 
course  of  the  function  k  is  precisely  similar  for  steel  and  nic  kel 
as  well  as  iron,  and  can  be  represented  by  the  same  empiric 
formula,  but  that  the  constants  of  the  formula,  even  for  two 
varieties  of  one  and  the  same  metal,  come  out  very  different  f* 

Professor  Biecke,  in  his  ''  Contributions  to  the  Knowledge  of 
the  Magnetization  of  Soft  Iron ''  (Pogg.  Ann,  vol.  cxlix.  p.  433), 
proposes,  instead  of  the  magnetizing-function  of  the  infinite 
cylinder,  to  consider  another  function  p,  which  has  the  same 
signification  in  reference  to  the  sphere. 

The  two  quantities,  referred  to  the  same  decomposing  force, 

*  '*  On  Magnetic  Permeability,  and  the  Maximum  of  Magnetism  of  Iron, 
Steel,  and  Nickel,"  Phil.  Mag.  August  1873,  p.  140.  The  term  "mag- 
netic permeability  "  is  used,  alter  Sir  W.  Thomson,  to  denote  the  quantity 
/t=l4-4iriir,  which,  as  ib  is  here  generally  much  greater  than  unity,  varies 
nearly  proportionally  with  k, 

t  Professor  Wiedemann,  when  discussing  my  work  (in  Galvanismus^ 
2nd  ed.  vol.  ii.  p.  518),  regards  the  function  which  is  calculated  from  ex- 
periments with  the  ring  as  another  magnetization-function,  not  to  be  con- 
founded with  that  obtained  from  experiments  with  *'  unclosed  systems." 
There  does  not  seem  to  me  sufficient  reason  for  this  distinction.  Residual 
magnetism,  which  is  here  in  question,  is  present  in  burs  also.  If  we  con- 
sider a  veiy  thin  and  lon^  bar  and  a  ring,  both  magnetized  uniformly,  the 
difference  between  them  m  relation  to  the  residual  magnetism  is  hardly  to 
be  reckoned  considerable.  The  demagnetizing  force  proceeding  from  the 
mass  of  its  iron  wiU  in  the  ring  be  equal  to  nil;  in  the  bar  it  is  a  small 

CO 

quantity,  of  the  order  of  ~p,  where  a>  is  the  cross  section,  and  /  the  length 

of  the  bar.  (Maxwell,  '  Treatise  on  Electricity  and  Magnetism,'  vol.  ii. 
p.  67.)  In  both  cases  an  external  force  is  requisite  in  order  to  expel  the 
residual  magnetism.  If  we  always  observe  the  reversal  of  the  magnetism 
of  the  iron,  the  calculation  of  k  is  only  to  this  extent  vitiated  by  the  residual 
magnetism,  that  a  certain  portion  of  the  reversed  decomposing  force  is  ex- 

E ended  in  discharging  it.     But  M.  Wiedemann's  own  experiments  with 
ars,  and  those  of  Poggendorff  with  closed  systems  (Wiedemann,  /.  c.p.519), 
show  that  that  portion  is  only  very  little. 

A  survey  of  the  numbers  obtained  by  Mr.  Rowland,  partly  with  bars, 
partly  with  rings,  establishes  that  the  most  essential  cause  of^^  their  differ- 
ence is  not  the  form,  but  the  quality  of  the  material. 


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202         Prof.  A.  Stoletow  on  the  Magnetxzation^Fimctumi 
are  connected  by  the  relation 


P- 


49r      1 
3   ■*■* 


The  function  py  he  says,  deserves  the  preference  because^ 
"  within  a  very  large  sphere  of  magnetizing  forces^  it  possesses 
a  nearly  constant  value  for  all  sorts  of  iron  '^  (/.  c.  p.  435).  The 
values  of  j9  calculated  by  M.  Riecke  from  his  own  and  others' 
experiments  do  in  fact  accord  very  well;  they  give  (p.  470)  as 
mean  value  for  moderate  decomposing  forces  the  number  0*2372^ 
and  as  maximum  value 

;>=0-2382. 

The  purpose  of  the  present  note  is  to  bring  out  that  these 
results  are  self-evident,  and  the  above  numbers  have  a  very 
simple  meaning ;  they  are,  namely,  pretty  close  approximations 
to  the  number 

^  =0-2387, 

47r 

which  is  obtained  as  the  upper  limit  of  p  when  we  put  A:=  oo, 
and  consequently  represents  the  ideal  maximum  of  p.      With 

moderate  decomposing  forces  t  is  always  small  compMfed  with  — 

(since  A  here  lies  somewhere  between  20  and  200*),  and  may,  in 
the  first  approximation,  be  neglected.  On  this  account  p  remains 
always  nearly  constant  and  independent  of  the  quality  of  the  iron\. 
Indeed,  for  every  other  strongly  magnetic  material,  about  the 
same  value  of  j9  would  result ;(. 

From  this  we  see,  on  the  one  hand,  that  the  numbers  calcu- 
lated by  M.  Riecke  furnish  a  fair  confirmation  of  the  theoretical 
consideration ;  but,  at  the  same  time,  we  see  that  the  quantity  p 
is  very  little  suitable  for  characterizing  the  magnetizability  of  a 
material,  since  for  the  sphere  the  influence  of  the  quality  of  the 
substance  nearly  vanishes  before  the  influence  of  the  form.  It 
can  be  proved  that  this  holds  good  generally  for  every  body  the 

*  For  my  iron  ringthe  maximum  of  k  wat  =>  174 ;  with  the  kinds  of  iron 
investigated  by  Mr.  Rowland  it  was  in  nearly  every  case  higher,  and  in  one 
case  reached  the  value  Ar=4d9  {fk^bSXb). 

t  A  brief  note  in  reference  to  this  I  find  in  Wiedemann's  Gahamtmrns^ 
2nd  ed.  vol.  ii.  p.  403. 

X  For  a  ring  of  annealed  nickel  Mr.  Rowland  found  the  maximum  of 
its  24  (/iss305).  According  to  this,  even  for  nickel  (at  its  maximum  of 
inagnetizability)  p  may  reach  the  value  0*2364.  For  sted  the  approxima- 
tion to  the  absolute  maximum  0*2387  becomes  still  closer,  and  holds  be- 
tween wider  Umits  of  the  decomposing  force. 


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of  various  Iron  Bodies.  203 

dimensions  of  which  in  all  directions  are  of  the  same  order*.  In 
order  to  calculate  it  priori,  with  satisfactory  accuracy,  the  mag- 
netization of  bodies  so  formed,  a  rough  estimation  of  the  coeffi- 
cient k  is  sufficient.  The  magnetization- functions  of  such  bodies, 
ascertained  by  experiments,  will  always  exhibit  much  less  varia- 
bility than  that  of  a  thin  bar  or  ring,  of  a  thin  plate  or  scale, 
and  may  almost  be  regarded  as  constant.  But  if,  starting  from 
such  mean  value,  we  try  to  calculate  the  magnetization  of  any 
body  of  the  category  last  mentioned,  we  may  arrive  at  very  in- 
accurate results ;  for,  with  bodies  one  or  two  dimensions  0/ which 
are  very  small  in  comparison  with  the  third,  the  tangential  compo- 
nent  of  the  magnetic  moment  will,  with  the  same  decomposing 
force,  increase  proportionally  with  kf.  The  influence  of  the 
specific  qualities  of  the  substance  appears  here,  therefore,  in  full 
intensity.  If  we  wish  to  bring  such  bodies  also  within  the  range 
of  our  considerations,  we  must  take  into  account  the  specific 
quality  of  the  substance,  and  the  knowledge  of  the  magnetiza- 
tion-functions of  bodies  of  this  sort  will  be  indispensable.  The 
function  k  perfectly  suffices  for  this  purpose,  and  has  the  advan- 
tage that  in  it  abstraction  is  made  of  the  transverse  dimensions 
of  the  thin  body. 

Those  bodies  the  dimensions  of  which  are  of  different  orders 
of  magnitude  play  a  peculiar  part  in  several  branches  of  physics. 
In  hydrostatics  their  theory  is  most  essentially  conditioned  by 
the  capillary  forces.  In  the  science  of  elasticity  they  require  a 
special  method  of  treatment ;  in  that  of  paramagnetic  magneti- 
zation they  make  a  very  precise  knowledge  of  the  magnetization- 
functions  absolutely  indispensable. 

Christmai  (O.  S.)  1873. 

*  Compare  pp.  66-67,  vol.  ii.  of  Maxwell's  Treatise — for  example, 
"  When  ic  18  a  large  positive  quantity,  the  magnetization  depends  princi- 
pally on  the  form  of  the  body,  and  is  almost  mdependent  of  the  precise 
value  of  «c,  except  in  the  case  of  a  longitudinal  force  acting  on  an  ovoid  so 
donated,"  &c.  (p.  66),  We  always  presuppose  here  that  the  magnetiza- 
tion IS  uniform. 

Jc 

t  More  strictly,  proportionally  with  TTTZt  where  c  is  a  number  vanish- 
ing with  the  transverse  dimensions,  and  the  value  of  ^  is  not  referred  to  the 

T 
whole  tangential  force  of  decomposition  T,  but  to  TXT'*    For  a  limited 

bar  €=0.  These  considerations  explain,  for  example,  the  experiments  of 
Von  Waltenhofen  on  the  magnetization  of  bundles  of  thin  wires,  thin- 
walled  tubes,  &c.  (Wiedemann's  Galvanismus,  2nd  ed.  vol.  ii.  p.  430).  The 
great  power  of  the  magnets  composed  of  thin  bands  of  steel  (rubans  d'acier) 
of  M.  Jamin  ( Comptes  Rendus,  vol.  Ixxvi.  p.  789)  appears  also  to  stand  in 
relation  therewith  (compare  especially  art.  X.  p.  794). 


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[    204    ] 

XXXI.  On  Tides  and  Waves,— Deflection  Theory. 

By  Alfred  Tyloe,  F,G.S. 

[With  Three  Plates.] 

To  the  Editors  of  the  Philosophical  Magazine  and  Journal. 

Gentlemen^  London,  August  15th,  1874. 

I  SHOULD  be  glad  if  any  of  your  readers  will  send  me  a  re- 
ference to  any  work  of  authority  in  which  there  is  any  direct 
statement  of  the  height  of  the  level  of  the  ocean  (say  the  central 
Atlantic)  compared  with  high-water  mark  on  the  east  and  west 
coasts  of  Ireland  and  England.  This  is  an  important  point  in 
the  general  theory  of  the  tides^  a  subject  I  am  about  to  dis- 
cuss. The  view  I  shall  advocate  is  that  the  level  of  the  ocean  is 
nearly  represented  by  high -water  mark  on  coasts  and  bays  where 
there  is  free  access  of  the  tide  and  a  channel  without  a  sudden 
taper.  Mr.  E.  Roberts^  of  the  Nautical  Almanac  OfiSce,  editor 
of  the  Reports  of  the  Tidal  Committee  of  the  British  Associa- 
tion^ informed  me  last  month  he  was  not  aware  of  any  statement 
in  print  on  good  authority  on  this  point.  The  only  opinion  I 
have  on  this  subject  is  from  Professor  6.  G.  Stokes^  F.R.S.  (and 
that  is  an  unprinted  one*),  who  wrote,  "  Nobody  maintains  that 
the  general  level  of  the  ocean  is  that  of  low  water ;  it  is  the 
mean  between  high  and  low,  except  in  shallow  channels  &;c., 
where  it  is  not  the  exact  mean/^  In  the  absence  of  further 
authorities  I  shall  give  my  deflection  theory  of  tides. 

In  Plates  II.  and  III.  I  give  a  drawing  of  what  I  suppose  is  the 
relation  of  high  and  low  water  on  the  coast  and  in  estuaries  and 
channels  to  that  of  the  sea.  I  show  that  the  level  of  the  central 
ocean  approximates  to  mean  high-water  mark  on  the  coast  of 
Ireland,  and  is  about  4  feet  above  the  English  Ordnance  Datum, 
which  datum  may  be  treated  as  an  arbitrary  line,  being  only  the 
mean  level  of  the  sea  at  Liverpool,  Penzance,  and  Falmouth,  all 
places  in  which  the  tide  is  affected  by  the  converging  contour 
of  the  coast. 

The  velocity  of  the  central  ocean- stream,  if  reduced  by  the 
inequalities  of  the  sea-bottom  at  a  different  ratio  to  the  depth, 
would  cause  the  water  to  heap,  and  vice  versd.  I  do  not  think 
it  does  heap  perceptibly  until  near  the  coast,  and  then  in  very 
different  degrees  (see  Plates  II.  and  III.).  When  the  increase 
of  velocity  exactly  balances  the  decrease  of  depth ;  that  is,  using 
Y  and  v  for  the  old  and  new  velocity,  and  I  and  t  for  the  re- 
spective distances  from  the  centre  of  the  earth, 

V       n 
when  I  =  t,  then  —  =  ^ (1) 

*  In  some  remarks  about  the  views  expressed  in  Plates  IL  and  IIL  sent 
to  him  for  examination,  March  7;  1874. 


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RED    TYJnn 


f  1 


Median/ 


-"•^^'SS^- 


22[flia5&: 


*W^^ 


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Mr.  A.  Tylor  on  Tides  and  Waves.  205 

This  is  the  equatioo  to  equilibrium  of  the  ocean-surface  in  the 
case  where  no  interfering  currents,  caused  by  difference  of  tern- 
perature  in  the  ocean,  are  present*.  A  complete  oceanic  tide 
stretches  from  coast  to  coast,  and  is  always  divided  into  three 
regions  (central,  anterior  flowing,  and  posterior  ebbing),  re- 
versing direction  each  six  hours ;  that  is,  in  the  part  where  there 
was  propulsion,  aspiration  succeeds,  and  vice  versd.  A  perfect 
tide  would  stretch  over  a  space  on  parallel  of  latitude  repre- 
sented by  the  rotation  of  the  earth  in  six  hours. 

The  mass  of  tbe  central  ocean  is  represented,  in  PI.  11.  figs. 
1  and  2,  and  PI.  III.  fig.  1,  as  moving  180  feet  per  hour  on 
the  average  of  each  tide  of  six  hours,  but  in  alternate  and  oppo- 
site directions.  A  movement  of  3  feet  per  minute  in  the  cen- 
tral ocean  20,000  feet  deep  would  communicate  a  velocity  of 
three  miles  an  hour  where  the  water  was  238  feet  deep,  by  the 
composition  of  forces.  1  suppose  that  this  slow  motion  in  a 
vast  mass  of  water  of  great  and  equal  depth  would  be  horizontal 
alone,  as  it  is  not  possible  to  suppose  vertical  motion  without 
creating  a  gap  below  or  behind  the  tidal  current.  The  hori- 
zontal motion  would  be  also  limited ;  for  the  sum  of  the  motion 
of  all  the  particles  of  water  in  the  Atlantic  tidal  stream  could 
not  exceed  the  area  of  the  gap  emptied  and  filled  on  the  oppo- 
site coasts  of  the  Atlantic  each  alternate  tide.  In  this  respect 
the  tide  is  like  a  wave,  the  relation  of  whose  movements  to 
the  size  of  the  gap  made  when  generated  is  clearly  shown  in 
fig.  1  (p.  216).  The  force  of  the  moon  will  be  estimated;  and 
the  relation  of  its  attraction  to  a  particle  on  the  ocean  is  shown 
in  fig.  4,  PL  IV.     The  direction  in  which  the  moon  can  affect 

*  From  the  equation  Q=AV,  using  Q  and  g  for  discharge  per  second, 
and  A  for  cross  section,  and  from  observation,  I  have 

i  -  vTi  •  ■  <^>- "-  '^'^¥1 "  V  -^/iA  ■  •  •  <^> 

from  which  I  obtain  a  new  equation  to  the  flow  of  water  in  uniform  motion 
— that  is,  only  when  V=r.    This  is 

i=KM) <^' 

which  applies  to  water  in  canals  in  uniform  motion,  as  in  fi^.  3,  Plate  III. 
The  tendency  of  every  river  is  to  approximate  in  all  parts  of  its  course  to  a 
uniform  mean  velocity.  The  river  carries  sand  and  mud  from  the  mountuios 
to  the  sea  along  its  channel  at  a  nearly  uniform  rate.  Increase  of  quantity 
of  water  flowing  at  any  point  balances  decrease  of  slope  throughout  all 
livers.  A  steamer  ascending  the  Rhine  meets  a  current  descending  at  one 
velocity  at  different  slopes.  This  is  proved  by  the  consumption  of  fuel 
being  equal  per  mile  from  the  sea  to  Mayence,  except  where  back-water 
on  one  side  increases  velocity  on  the  other,  or  where  shallows  retard  the 
ship.    I  do  not  find  (R  the  mean  hydrauUc  depth)  of  value  in  calculations. 


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206  Mr.  A.  Tylor  on  Tides  and  Wavu. 

particles  of  water  and  move  them  is  represented  in  a  new  manner. 
The  sun's  effect  can  be  calculated  similarly  to  the  moon^s. 

The  attraction  of  the  moon  when  in  a  vertical  line  would  not 
produce  any  horizontal  or  vertical  movement  in  a  particle  of 
water  below  it ;  and  the  attraction  could  not  produce  a  heap  of 
water  below  it  without  the  water  being  propelled  from  some 
point  of  the  ocean  on  which  the  rays  of  attraction  fell  at  an  angle 
less  than  90° ;  and  then  I  do  not  think  the  heap  could  exceed 
2  inches  in  height*,  for  reasons  which  will  be  given  hereafter. 

The  mass  of  the  moon  is  equal  to  a  spherci^of  118*75  miles 
diameter  of  the  same  density  as  the  earthy  and  situated  at  3956 
miles  from  the  point  to  be  attracted — that  is^  at  the  distance 
of  the  radius  of  the  earth.  The  circle  F  near  C  (fig.  4,  PI.  IV.) 
should  be  only  one  sixth  of  an  inch  if  drawn  to  scale.  It' 
is  shown  in  the  position  in  which  it  would  i«present  the  action 
of  the  moon  on  the  ocean  if  it  revolved  round  C  in  a  lunar 
month.  Thus  any  point  on  the  circumference  of  the  earth  must 
be  attracted  to  the  centre  of  the  earth  by  an  attraction  greater 
than  that  of  the  moon  to  the  same  point  in  the  ratio  of  295520 
to  ].  For  60*263«=8681,  and  60263  is  the  mean  distance 
of  the  moon  from  the  earth  ;  then  the  density  of  the  earth  is  to 
that  of  the  moon  as  1*647  to  1^  and  the  mass  of  the  earth  to 
that  of  the  moon  as  49*5  to  1.     Then 

3631  X  49-5  X  1647=295520; 

that  is,  the  effect  of  the  attraction  of  the  moon  in  a  particle  on 
the  surface  of  the  earth  (at  the  moon^s  mean  distance)  is  only 
^—^  of  that  arising  from  the  attraction  of  the  earth  itself  f. 

The  weight  of  any  body  on  the  earth  would  therefore  be 
lightened  in  that  ratio,  or  in  the  proportion  of  1  grain  to  4^ 
gallons  of  water  (70^000  grains  to  the  gallon),  the  moon  being 

*  This  is  a  different  case  altogether  from  that  of  tbe  estimate  of  coUec- 
tion  of  water  at  the  equator;  and  the  practical  test  given  above  is  better 
than'theoiy. 

t  This  IS  calculated  differently  in  a  note  to  page  628,  Herschers  *  Out- 
lines of  Astronomy/ 1873 :  the  cube  of  the  sun's  distance  is  erroneously  in- 
troduced into  the  calculation  for  finding  the  moon's  maximum  power  to 
disturb  the  water  in  the  surface  of  the  earth  ;  this  brings  the  relative  effect 
of  the  moon's  attraction  to-jyr^VTinr  of  K^s^vity,  according  to  Herschel. 
This,  however,  is  only  -^^  ot  the  real  quantity.  My  calculation  is  ac- 
cording to  the  following  law:— "Two  such  globes  would  (by  the  same 
proposition)  attract  one  another  with  a  force  decreasing  in  the  duplicate 
proportion  of  the  distance  between  their  centres  "  (Newton,  page  24,  edit. 
819).  If  Herschel's  figures  were  correct,  we  should  have  tides  of  3  inches 
on  our  coast  instead  of  12  feet  in  height.  Also  the  fictitious  moon  F  placed 
near  C  (fig.  4,  PI.  IV.^,  to  represent  the  effect  of  the  real  moon,  would 
have  only  a  diameter  of  34*03  miles,  and  contain  2^,629  cubic  miles  instead 
of  the  larger  quantity  mentioned  by  me  in  tbe  text.  , 


?; 


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Ph2lMag.&4.Vol48.Pl.m. 


MMIIs ~ 


tsgirw  oyer  ^tetBar-withMV  Iflsavpttydj^^ 
ter  mde^,runmjy  at^wMmey^^fetd^oiin. 

u     ,  „      •   supposed^  tahe ^tatUmary . 


NOTE  For  oalcuJUUxnf  rAoeuty  c^Wbitr  w 
itrdi/fbwUmjKUrMtdi^ArMeCa^ 

Thus,  v^  fO  ^.i   mr  y  "  36  J^.v .  or/uf& 


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Mr.  A.  Tylor  on  Tides  and  Waves.  207 

at  its  mean  distance.     The  attraction  of  the  moon  I  calculate  to 
be  one  fifteenth  greater  at  a  point  on  the  near  side  of  the  earth 
than  at  a  point  vertically  below  it  on  the  offside  at  the  antipodes. 
Every  day  the  change  of  position  of  the  moon  with  regard  to 
the  earth  would  affect  all  weights  on  the  surface  of  the  earth 
temporarily^  but  only  to  the  extent  of  1  grain  in  61  gallons^  a 
quantity  which  is  not  susceptible  of  measurement  by  a  balance. 
The  effect  of  the  moon^s  direct  attraction  is  really  very  small 
on  each  cubic  foot;  but  as  it  affects  water  at  the  bottom  of 
the  sea  nearly  as  much  as   on  the  surface^  it  amounts  to  an 
enormous  moving  force  when  a  stream  20^000  feet  deep  is  set 
in  motion.     It  is  only  perceptible  to  observation  when  motion 
is  accumulated  by  composition  at  certain  points^  such  as  where 
there  is  a  great  composition  of  forces^  as  in  soundings.    Navi- 
gators do  not  observe  the  motion  of  the  tide  except  near  the 
coast.     I  calculate  the  amount  in  the  following  manner.     If 
the  effective  force  of 'the  moon  has  to  be  multiplied  eighty-four 
times  to  raise  a  12-foot  tide  at  a  point  of  the  coast  where  the 
sea  is  238  feet  deep^  then  the  direct  effect  of  the  moon's  attrac- 
tion on  water  238  feet  deep  would  only  be  \  foot^  or  something 
under  2  inches.     Thus  T  consider  2  inches  is  the  greatest  height 
that  the  moon  could  possibly  raise  the  level  of  the  sea  under  it 
with  238  feet  depth  of  water^  |~J-  of  the  elevation  of  12  feet 
being  the  effect  produced  in  deeper  water  by  the  moon  and 
sun,  transferred  by  the  composition  of  forces  to  shallow  water. 
The  drawings  (figs.  1,  2,  and  3,  PI.  IV.)  from  standard  works 
on  tides  are  therefore  great  exaggerations  by  their  authors ;  and 
the  descriptions  accompanying  them  would  lead  any  one  to 
suppose  a  great  heap  of  water  could  be  rapidly  accumulated  in 
the  central  ocean  by  vertical  attraction  on  deep  water.     The 
authors  do  not  specify  how  the  water  is  obtained,  or  whence  it  is 
comes,  or  the  data  by  which  they  prove  such  a  heaping  up 
possible  as  is  proposed  by  the  equilibrium  theory. 

Time  is  the  essence  of  such  an  operation,  which,  if  done  at 
all,  must  be  completed  in  six  hours,  or  a  contrary  current  would 
set  in.  The  heaping-up  movement,  to  keep  up  with  the  rota- 
tion of  the  earth,  would  have,  in  the  latitude  of  Brest,  to  make 
water  flow  at  11*3  miles  per  minute,  which  is  clearly  impossible. 
It  is  not,  therefore,  surprising  that  the  effect  of  the  tidal  wave  is 
hardly  perceptible  at  oceanic  islands,  whereas,  if  figs.  1, 2,  and  3, 
PI.  IV.,  were  correct,  it  ought  to  be  as  large  there  as  on  the 
mainland  coast. 

Fig.  1,  PI.  IV.  is  an  explanation  of  the  tides  copied  from  the 
'  Penny  Cyclopsedia ; '  figs.  2  and  3,  PI.  IV.,  are  from  Dr.  Lard- 
ner's  '  Astronomy,'  pp.  324-5 ;  and  my  own  view  is  given  in 
fig.  4;  so  that  the  reader  may  compare  the  different  theories. 


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208  Mr.  A.  Tylor  on  Tides  and  Waves. 

If  fig.  4,  PI.  IV.,  is  correct,  there  can  be  no  great  heaping  up 
of  water  or  any  tidal  wave  generated  in  one  direction,  as  has 
been  sometimes  assumed ;  for  I  show  that  the  action  of  the  tide 
is  a  reciprocating  action,  and  has  as  much  motion  from  west  to 
east  as  from  east  to  west. 

The  assumption  of  a  great  heap  of  water  travelling  in  one 
direction,  or  producing  a  certain  amount  of  retardation  of 
the  rotary  movement  of  the  earth,  quite  unbalanced  by  ac- 
celeration, has  been  taken  as  a  serious  fact;  many  writers 
of  reputation  have  supposed  that  the  rotation  of  the  earth 
must  be  affected  by  this  hypothetical  wave-action  in  one  di- 
rection. 

My  view  of  the  general  theory  of  the  tides  (fig.  4,  PI.  IV.) 
differs  materially  from  those  generally  accepted ;  and  I  cannot 
understand  the  existence  of  an  intumescence  (shown  in  figs.  1, 
2,  and  3,  PI.  IV.)  under  the  moon  at  all  if  the  subject  is  treated 
in  the  ordinary  manner  of  reasoning. 

I  entirely  disbelieve  in  tidal  action  having  the  smallest  effect 
on  the  rotation  of  the  earth.  It  is  a  balanced  action.  The  sun 
might  produce  currents  by  unequally  heating  water,  which 
might  affect  the  surface-level  of  the  sea  and  cause  inequalities  ; 
but  of  this  there  is  no  positive  evidence.  I  show  by  fig.  3,  PI.  III. 
that,  under  certain  circumstances  observed,  a  curi'ent  may  travel 
against  the  slope  of  the  surface.  This  I  noticed  in  your  Journal 
in  1853.  The  existence  of  a  current  is  of  itself,  therefore,  no 
proof  of  what  is  the  direction  of  the  slope  of  the  surface.  I  find 
that  an  elevation  of  level  of  2  inches  on  the  east  maintained  over 
the  west  side  of  the  Atlantic,  or  ince  versd,  where  water  is  very 
deep,  would  generate  a  current  of  3  feet  per  minute  in  the  ocean 
in  the  direction  of  the  slope,  supposing  the  Gulf-stream  did 
not  intervene  and  there  was  no  tidal  action.  The  western  water 
would  take  5  years  to  cross  the  Atlantic  at  a  speed  of  3  feet 
per  minute,  to  reestablish  equilibrium.  If  the  difference  of  level 
were  produced  by  luni-solar  action,  it  would  cause  no  current 
until  the  force  creating  it  was  withdrawn. 

If  58  miles  per  hour  is  the  greatest  velocity  a  surface- wave 
could  travel  at  in  the  deepest  part  of  the  Atlantic,  such  an  in- 
tumescence, even  if  maintained,  would  have  only  proceeded  348 
miles  before  the  moon's  influence  would  be  exerted  against  its 
motion.  The  great  earthquake-impulse  of  Lisbon  in  1755,  pro- 
ceeding through  deep  water,  did  not  travel  to  Barbadoes  faster 
than  6  niiles  per  minute;  and  an  intumescence  of  equal  force  or 
impulse  created  on  the  W.  coast  of  America,  in  the  latitude  of 
Brest,  would  meet  contrary  luni-solar  attractions  when  half- 
way across  the  Atlantic.  No  intumescence  could  be  raised  in 
deep  water  without  forming  a  gap  below. 


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*teOT/ 


Phil.Mag.S.4Afol.48.H.IV. 


Qiope,  is  fapponed  to  i«r?oWe  in  the  circle  A.E.B.  W  in  24  > 
fhe  sMne  niean  yeloeity  each  24  hoan,)»is  retarded  and 
at  the  exact  lunar  hours  marked,  but  within  them 
VerticaL 


>od  tide. 


loean  below  the  speed  of  the  earth-baain  holding  it, 
_iiP9Fy:Aot  the  rotation)  at  ebb  tide  shown  in  B. B.  and  W.  A,, 
Jl/.  J/,    isesca  flowing  ti de  as  in  A.  B.  and  B.  W.  Fig.  4  plate  IV. 


^ 


ition  in  alternate  directions,  the  real  mean  velocity 

the  one  direction,  and  only  difference  of  speed  is 

>oking  from  one  to  the  other  only  can  estimate  the 

it  of  America,  for  there  the  ebb  tide  is  in  tbe  direction 


oceanic  water  and  a  flowing  tide  before  it  (propulsion ) . 


I 


I  present,  Jointly  attracted  by  Mi.Mii,  attraction 
'/?tnC/^e  time.   The  resultant  motion  of  the  particle  P  n.  is 
Jf,JlT,   article  P.  IV  is  in  a  contrary  direction,  because  th« 


^through  the  Earth,  deflected  by  meeting  the  curved 
Lhich  accelerates  the  ocean  in  the  direction  of  B  to  W. 

Aon  of   £  to  B,  and  the  force  M.  iv  being  deflected 
on  to  P.  vm  and  retards  water  in  tbe  quadrant  W  A. 


Itw." 


kuses  alack  tide  at  low  and  high  water. 

>f  the  Barth  deflecting  attraction  rays  at  vari(>us 


near  C,  Pig.  4,  plate  iv  supposed  when  revolving 

M^  do. 


»een  accelerated  above  US  per  minute  back  to  that 
)w  water  for  convenience.  1  omit  the  action  of 
ience. 


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Mr.  A.  Tylor  on  Tides  and  Waves.  209 

In  fig.  4,  PI.  IV.^  I  take  a  particle  of  water  at  certain  points  on 
opposite  hemispheres^  and  show  the  direction  of  the  resultants 
of  the  two  forces  (the  moon  and  earth's  attraction)  and  the  pro- 
bable deflection  of  the  moon's  attractive  rays  in  passing  through 
the  earth.  Sir  J.  Herschel  (p.  528)  only  gives  one  position  on 
his  Plate  (p.  464),  and  leaves  it  to  the  reader  to  try  the  position 
of  particles  on  other  parts  of  the  circle  and  find  their  direction. 
I  have  tried  to  do  so  according  to  his  rule,  and  find  that  his 
diagram  would  only  apply  to  the  moon's  attraction  by  the  earth 
at  such  an  immense  distance  that  gravity  could  be  considered  as 
acting  to  and  from  single  points,  viz.  the  centres  of  the  two 
attracting  bodies,  and  surface  attractions  need  not  be  considered. 
Now  the  case  of  the  tides  is  clearly  that  of  a  point  or  particle 
at  the  surface  of  the  earth  being  attracted  by  the  two  centres  of 
the  earth  and  moon.  IlerschePs  figure  (p.  464)  is  not  appropri- 
ate to  the  conditions  of  the  tides ;  iot  it  has  no  special  relation 
to  surface  attraction  at  all.  If  it  proved  any  thing  about  tides, 
it  would  prove  there  would  only  be  a  tide  every  twenty-four 
hours.  On  the  contrary,  in  fig.  4,  PI.  IV.,  I  take  into  account 
the  deflection  of  the  rays  of  attraction  on  entering  the  earth, 
and  find  that,  if  they  pass  through  the  earth  with  the  rapidity 
of  light,  when  they  reach  the  other  hemisphere  they  cause  a 
twelve-hours  tide,  simultaneously  produced  to  that  on  the  oppo- 
site side  of  the  globe. 

I  have  proved  by  analyzing  the  experin^euts  on  waves 
by  J.  S.  Russell  and  by  Darcy,  that  the  velocity  measured  in 
feet  per  second  of  any  wave  when  generated  does  not  exceed 
three  times  the  cube  root  oi'  the  depth  of  the  water  it  was  gene- 
rated in,  measured  in  feet;  that  is,  v=B\/p,  a  new  formula, 
which  answers  both  for  small  and  great  depths,  the  usual  for- 
mulae giving  results  much  too  high  for  waves  generated  in  deep 
water. 

.  Mr.  W.  Parkes  (Phil.  Trans.  1868)  suggests  that  the  al- 
4emate  tides  are  produced  in  different  hemispheres,  and  that 
the  evening  tide  which  reaches  Kurrachee  twelve  hours  after 
the  morning  has  travelled  a  greater  distance.  This  does  not 
seem  probable;  nor  does  he  give  any  evidence  on  the  point. 
Then,  with  regard  to  the  diurnal  variations  of  the  two  tides, 
Mr.  W.  Parkes  (p.  686y  says  the  diurnal  inequalities  disappear 
when  the  attracting  bodies  are  in  the  plane  of  the  equator.  It 
appears  to  me,  from  the  observations  at  Kurrachee,  that  when 
the  diurnal  irregularity  of  the  high-water  points  is  at  its 
maximum,  the  diurnal  irregularity  of  the  low-water  points  is 
at  its  minimum,  and  vice  versd.  Curiously  enough,  at  Kurra- 
chee the  mean  diurnal  low-water  irregularity  is  about  2  feet, 
against  about  1  foot  (the  mean  diurnal  irregularity  of  the  high 

P/iiL  Mag.  S.  4.  Vol.  48.  No.  317.  Sept.  1874.  P 


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310  Mr.  A.  Tylor  en  Tides  and  Waves. 

water).  Tbat  is,  instead  of  tV  of  the  height  of  this  lunar  portion 
of  the  tide  representing  the  diurnal  irregularity  (which  I  con- 
sider is  the  mean  of  the  world),  at  Kurrachee  the  tides  are  so 
exceptional  that  the  diurnal  irregularity  amounts  at  low  water  to 
if  and  at  high  water  to  |  of  the  total  height  on  the  average  of 
the  tides  for  a  month,  lliis  opposite  action  cannot  be  owing 
to  the  position  of  the  attracting  bodies  in  the  respective  tides 
being  in  the  plane  of  the  equator. 

I  would  observe  that  the  deep  central  ocean  without  any 
vertical  tidal  movement  or  tide-wave  observed  is  certainly  forty 
times  as  large  as  the  shallow  coast^sea,  where  a  rise  of  tide  is 
observable.  The  composers  of  figs.  1,  2,  and  3,  PI.  1V.|  seem 
to  r^ard  the  coast  alone,  which  I  consider  the  exception. 
They  do  not  seem  to  think  of  the  tidal  conditions  in  the  great 
mass  of  the  ocean  at  all  in  forming  their  theory* 

It  appears  from  figs.  1  and  2,  PI.  II.,  and  fig.  1,  PL  III., 
from  observation,  that  the  level  of  the  sea  at  high  water,  even 
in  the  tidal  estuary  of  the  lliames,  is  only  raised  5  feet,  and  in 
that  of  the  Clyde  1  foot,  above  the  central  ocean. 

The  high-water  points  from  Falmouth  to  Sheemess  are  nearly 
level;  they  only  deviate  1  foot  in  500  miles  from  a  straight  line. 

The  fact  has  not  been  sufficiently  considered,  that  water  in 
open  channels  can  be  moved  under  certain  conditions  against 
gravity,  and  that  the  great  central  mass  of  the  ocean  swinging 
backiN^irds  and  forwards  every  six  hours  is  one  of  the  forces  that 
can  easily  overeome  gravity  when  producing  a  slow  current.  As 
early  as  1868  I  gave  a  drawing  in  your  Journal  (p.  259)  of  the 
bottom-water  outside  the  bar  of  the  Mississippi  being  raised  to 
the  surface  16  feet  against  gravity  by  the  current  of  fresh  water 
flowing  outwards,  partly  impelled  by  gravity  (propulsion)  and 
partly  sucked  or  drawn  by  the  tidal  water  in  front  of  it  (aspira- 
tion) :  see  fig.  4,  PL  III.  I  still  believe  that  the  tidal  current 
acts  like  the  piston  of  a  pump,  and  reduees  the  pressure  in  its 
rear,  and  draws  or  sucks  out  the  coast-water  after  it  in  the  ebb- 
tide, and  piQshes  the  water  back  again  to  fill  up  the  gap  when 
its  notion  is  reversed  by  the  luni-solar  force  in  the  flowing  tide. 
I  first  observed  evidence  of  this  action  on  the  bars  of  rivers,  and 
represent  it  in  fig.  2,  PI.  III.  As  the  water  in  the  Mississippi 
is  100  feet  deep  at  a  comparatively  short  distance  behind  the 
bar  BC,  and  is  in  motion  from^  top  to  bottom,  the  lower 
water  is  evidently  drawn  over  the  bar  and  up  an  asceut  of  84 
feet  against  gravity,  by  the  pressure  of  the  water  at  B  C  on 
the  bar  being  reduced  by  the  tide  or  mass  of  oceanic  water  mo- 
ving steadily  before  it.     Motion,  of  course,  ensues  in  the  direc- 

*  Humpbrys  and  Abbott  record  rapid  motion  at  the  bottom  at  Carrol- 
iqn,  page  149. 


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Mr.  A.  Tylor  on  Tides  and  Waves.  211 

tion  of  least  pressure ;  and  that  happens  to  be^  as  far  as  the  upper 
part  of  the  water  is  ooneerned,  against  gravity,  and  is  similar  to 
what  happens  in  a  mill-raee  (fig.  8,  PI.  III.).  This  action, 
which  takes  place  at  the  mouths  of  all  large  rivers,  is  a  clue  to 
the  tidal  movements.  It  is  true  that  in  the  Severn  at  Beachley 
the  high-water  level  of  spring  tides  is  25  feet  above  the 
Ordnance  Datum,  and  21  feet  above  the  level  of  the  central 
ocean.  But  this  is  an  exceptional  case  that  can  be  explained. 
At  Beachley  at  high  water  the  cross  section  is  400,000  sup.  feet, 
and  at  low  water  only  25,000  sup.  feet  (see  fig.  1,  PI.  II.)- 

At  Stonebench,  36  miles  higher,  there  is  only  a  cross  section 
of  240  feet,  and  a  depth  of  8  feet  at  low  water. 

The  cross  section  at  Beachley  is  not  a  tenth  of  the  sexstion  a 
few  miles  lower  down  in  the  Bristol  Channel. 

The  exceptional  height  of  the  tide  there  is  solely  due  to  the 
funnel  shape  of  the  c^nnel,  caused  by  the  hard  recks  that  pre- 
vent the  tideway  being  excavated  to  the  usual  form.  This 
exception  proves  the  rule.  I  compare  the  ebb-tide  to  the  action 
of  a  mill-stream,  thus  i-^ 

Fig  8,  PL  III.,  represents,  from  actual  observation,  a  case 
of  water  moving  against  gravity  in  an  open  channel,  and  against 
the  direction  of  the  slope  of  the  surface  of  the  water.  The 
atream  of  water  passing  over  the  weir  at  B  falls  in  a  thin  stream  at 
great  velocity  to  C^.  Here  it  changes  its  direction  and  the  current 
is  against  the  slope  of  the  surface,  vis.  towards  D^  instead  of 
towards  C^,  which  would  be  the  direction  of  gravity.  The 
stream  D  E  in  uniform  motion  niduces  the  pressure  at  D  and 
draws  the  water  from  C  after  it— just  as  the  great  central 
oceanic  stream  represented  in  figs.  1  and  2,.  PI.  II.,  and  in 
fig.  1,  Plate  III.,  draws  the  coast-water  westwards  and  forms  a 
gap  which  is  filled  by  the  tide,  the  oceanic  stream  having  reversed 
its  direction  in  six  hours,  as  shown  in  fi^«  %  PL  IV.,  by  luni- 
solar  attraction  pushing  on  to  the  coast-hne  the  flowing  tide. 

My  explanation  of  Che  luni-solar  attraction  in  fig.  4,  PL  IV., 
is  placed,  adjoining  the  drawing. 

It  will  be  observed  I  omit  in  the  diagram  (fig.  4,  PL  IV.)  the  eits* 
tomary  theoretical  intumescences  opposite  to  each  other  movine 
with  the  moon,  but  through  eadi  of  which  every  part  of  the  earth 
is  supposed  to  pass  daily,  as  in  figs.  2  and  8,  PL  IV«,  and  I  show 
an  alternating  tide  in  the  ocean  itself  instead,  in  fiig.  4.  I  con- 
fess I  cannot  follow  the  supposed  changes  of  form  of  the  ocean- 
surface  in  figs.  1, 2,  and  8,  PL  IV.,  nor  imagine  either  that  such 
movements  could  possibly  occur,  or  that  they  .would  at  all  de- 
ncribe  the  tidal  changes  at  any  point  of  the  globe  as  known  to 
obs^rvera.  I  remark,  the  writera  give  no  dimensions  of  the  in- 
tumescences, or  calculate  the  force  to  convert  the  circle  ab  into 

P2 


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212  Mr.  A.  Tylor  on  Tides  and  Waves. 

the  ellipsoid  a,  by  M.  Arago  very  justlv  wrote  that  '^  details  are 
the  touchstones  of  theories ;''  and  all  details  are  absent  in  the 
well-known  articles  on  this  subject.  In  fig.  1  the  earth  is 
represented  as  a  circle^  and  the  ocean  as  an  ellipsoid*  In  figs. 
2  and  3  the  water  is  the  circle^  and  the  earth  the  ellipsoid. 

According  to  figs.  1,  2,  and  8,  PI.  IV.,  the  velocity  of  the 
tide  would  be  equal  at  high,  low,  and  half  tide  to  any  observer 
on  the  earth. 

The  greatest  action,  on  the  contrary,  is  shown  to  be  at  the  half 
tide,  both  ebb  and  flowing,  in  my  diagram,  fig.  4,  PI.  IV.  Cap- 
tain Beechey*  remarked  that  the  velocity  of  the  current  was 
greatest  at  half  tide ;  and  this  disproves  any  theory  in  which 
the  tide  is  supposed  theoretically  equally  strong  at  all  parts. 

Dr.  Lardnerf  explained  his  diagrams,  figs.  2  and  3,  PI.  IV., 
by  stating  that  the  moon  forces  down  the  water  at  the  sides  at 
right  angles^o  her  direction,  and  raises  it  at  the  two  ends  of  its 
diameter  pointing  to  her.  In  figs.  2  and  3,  PI.  IV.,  the  moon 
pulls  the  water  in  one  hemisphere  and  pushes  it  away  in  the 
other.  This  is  the  first  time  that  the  property  of  repulsion  or 
forcing  has  been  attributed  in  this  manner  to  the  heavenly  bodies. 
He  shows  an  exactly  opposite  direction  of  forces  on  the  near  and 
far  side  of  the  earth  prodbced  at  the  same  moment  by  the  moon. 

Notwithstanding  any  language  that  may  be  used  to  make 
figs.  1,  2,  and  8,  PI.  IV.,  appear  to  satisfy  the  actual  tidal  con- 
ditions, it  will,  I  think,  be  evident  to  the  reader  that  the  posi^ 
tions  of  the  forces  as  drawn  are  not  in  accordance  with  the  ordi- 
nary laws  of  mechanics.  Herschel  refers  the  reader  to  his 
drawing  (Astronomy,  p.  461),  in  which  the  retardation  and  acce^ 
leration  of  the  moon  in  its  elliptic  orbit  round  the  earth  at  a 
mean  distance  sixty  times  the  radius  of  the  earth  is  proved  to  be 
according  to  the  law  of  equal  spaces  being  described  by  the  moon 
in  equal  times,  and  consequent  variation  of  motion. 

The  reader  is  recommended  by  Herschel  to  prove  the  accele- 
ration or  retardation  of  the  tides  from  the  diagram  (p.  464), 
which  is  really  impossible,  as  the  figure  relates  to  an  entirely 
different  case,  and  is  in  a  part  of  his  book  relating  to  the  motions 
of  the  moon.  It  is  admitted  that  the  moon  is  a  free  body  attracted 
at  a  great  distance  by  the  earth,  and  made  to  mo\  e  at  varying  velo- 
cities round  the  earth  in  a  lunar  month  at  a  rate  dependent,  among 
other  causes,  upon  the  relative  weights  and  distances  of  the  moon 
and  earth,  and  the  original  impetus  and  angle  at  which  these 
bodies  were  projected  into  space.  The  tidal  water,  on  the  con- 
trary, is  held  as- an  inseparable  mass  of  fluid  reposing  in  a  basin 
of  earth  ;  and  it  travels  at  the  same  uniform  speed  of  rotation  as 

♦  Phil.  Trans.  1851,  p.  711. 

t  Lardner*8  'Astronomy,'  p.  336. 


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Mr.  A.  Tylor  on  Tides  and  Waves.  213 

the  earthy  except  when  modified  in  velocity  to  a  very  small  ex- 
tent by  the  attraction  of  the  celestial  bodies,  producing  the  tides. 
The  two  cases  are  not  parallel,  and  the  diagram  mentioned  by 
Herschel  is  certainly  not  applicable  to  the  tides  at  all.  The 
oceanic  water  has  no  tangential  force  independent  of  the  earth ; 
for  two  points  in  the  ocean^  reaching  180°,  opposite  to  each  other 
are  at  the  same  distance  from  the  centre  of  the  earth,  and  are  in 
exact  equilibrium  if  the  difference  of  tidal  action  i&  left  out  of 
consideration.  I  think  the  authors  have  not  taken  into  consi- 
deration the  fact  that  the  rays  of  attraction  from  the  moon  to 
the  water,  when  the  water  is  screened  from  the  moon  by  the 
earth,  would  pass  through  the  earth,  in  order  to  reach  the  oppo- 
site side,  not  in  a  straight  line.  They  would  not  only  lose  force  of 
course  as  the  square  of  the  distance  increased,  but  I  think  no 
ray  or  vibration  or  impulse  or  line  of  attractive  force  could  fall 
upon  or  pass  through  a  curved  body  such  as  the  earth  at  an  acute 
angle  without  being  in  some  way  defiected  or  diverted  from  its 
direct  course  in  passing  through  the  earth  to  water  on  the  other 
side ;  and  the  reverse  is  true.  I  believe  a  vibration  of  any  kind,  or 
attraction-ray,  would  have  to  be  modified  in  its  direction  or  bent 
at  the  point  of  contact,  so  as  to  enter  the  surface  of  the  earth  at  a 
right  angle  to  a[tangent  of  the  curve  at  the  point,  as  shown  in  fig.  4. 

My  own  view  (PI.  IV.  fig.  4)  shows  slack  water  at  the  turn 
pf  the  tide  both  near  high  and  near  low  water;  but  of  course  these 
events  do  not  always  coincide.  When  the  luni- solar  attraction-rays 
fall  near  A  and  B  (fig.  4,  PI.  IV.),  they  are  evidently  deranged  and 
deflected  so  as  to  produce  very  little  effect ;  in  fact  the  state  of 
the  tide  near  those  points  is  what  might  be  called  bordering  on 
motion, which  state  accords  with  observation.  Although  the  angle 
M|P^R^  is  onljr  i"'07y  or  two  thirds  of  the  angle  M^^P^^R^,,  yet  the 
factual  effect  m  producing  tidal  motion  is  much  less  than  that 
proportion.  For  at  P  the  tidal  motion  is  being  reversed^  and 
the  speed  of  the  flowing  tide  has  to  be  created  from  slack  water; 
while  at  P^^  the  effect  of  attraction  from  M^^  is  to  accelerate  the 
tide  then  moving  freely  and  in  the  same  direction  as  it  has  been 
between  P^  and  P^^  and  also  in  the  line  of  the  earth's  rotation. 
The  actual  effect  in  velocity  theoretically  is  quite  four  times  as 
much  in  the  half  hour  near  P^,  as  at  that  near  P^ ;  and  this  accords 
with  observation.  The  angle  of  the  resultant  B^  is  found  thus. 
The  angle  M^P.C  is  88^  30?  4"=318604  seconds. 

The  force  M.P,  is  to  C  P,  as  1  to  295,520 ;  .'.  the  angle 

M|P^Bp  the  resultant,  equals     q,"  q^=F'07.     In  the  same 

manner  the  angle  M^^P^,B^^=1"*66.  The  depth  of  the  Atlantic 
(five  miles)  favours  movement  very  much,  as  there  is  room  for  the 
force  in  the  direction  A  B^  to  be  transferred  easily  into  the  direc- 


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214  Mr.  A.  Tylor  on  Tides  and  Waves. 

tion  P^,  E,  which  is  that  of  the  line  of  rotation.  In  an  inland  sea 
like  the  Mediterranean,  where  the  deep  water  is  6000  feet,  the 
movement  of  the  tide  on  the  coast  is  often  not  more  than  1  foot. 
There  are  7-feet  tides  in  one  or  two  places  in  the  Mediterranean 
where  the  contour  of  the  coast  is  like  onr  Bristol  ChanneL 

If  the  deep  water  in  the  Mediterranean  Sea  were  one  twelfth 
of  the  depth  of  that  in  the  Atlantic,  we  should  expect  a  1-foot  tide 
there  in  place  of  a  12-feet,  according  to  the  law  of  compositimi 
of  forces'!'.  The  peculiar  circumstances  of  the  Mediterranean 
make  the  tides  much  smaller  than  I  should  have  calculated  from 
the  experience  of  the  Atlantic.  Taking  6000  feet  as  the  basis  of 
the  deep  water  and  9  inches  as  the  tide,  diffusion  of  the  tidal  force 
from  deep  central  to  surrounding  shallow  coast-basins  seems  to 
absorb  i  of  the  force.   The  proportion  of  deep  water  is  very  small. 

The  Mediterranean  standard  of  rates  of  depths  of  ocean  to 
height  of  tide  along  its  coasts,  seems  to  match  more  with 
Pacific  and  west*coast-of- America  standards  than  with  the  obser- 
vations on  the  eastern  Atlantic  coast.  The  European  tides  seem 
exi^gerated,  even  when  compared  with  the  east  coast  of  America* 
This  may  be  explained  by  less  diffusion  c£  tidal  force  and  the 
contour  of  the  sea- bottom  on  our  coast  being  more  favourable 
to  receiving  impulses  giving  velocity  to  the  coast-water  than 
that  on  the  east  coast  of  America.  For  want  of  space  I  have 
hardly  been  able  to  allude  to  the  solar  influence  of  the  tides, 
which  differs  in  some  respects  from  the  lunar  relations. 

Hie  diurnal  and  semidiurnal  tides  are  known  to  vary  about 
4  inches  in  an  8-feet  tide.  Then,  supposing  that  2  feet  of  the 
8  feet  is  caused  by  solar  attraction,  the  variation  is  one  fifteenUi 
of  the  height  due  to  lunar  action.  If  the  tide  generated  in  deep 
water  is  twelve  lunar  hours  reaching  a  part  of  the  coast,  the  greater 
alternate  twelve-hours'  tide  will  become  the  lesser  of  tl^  two. 
There  are  many  other  considerations  to  take  into  account  which 
materially  modify  the  sise  of  the  alternate  tides  at  different  parts 
of  the  month ;  and  I  do  not  put  forward  mv  own  view  with  any 
pretensions  to  improve  the  prediction  of  tiaes,  which  indeed  is 
already  perfectlv  done  by  the  machine  invented  by  Sir  W. 
Thomson  and  Mr.  E.  Roberts  of  the  Nautical  Almanac  Office. 
What  I  wish  to  do  is  to  give  an  explanation  of  a  theory  of  the 
tides  which  shall  accord  with  the  physical  facts.  Supposing 
the  point  E  is  thirty  diameters  of  the  earth  from  the  moon  on 
any  day,  then  the  point  W  will  be  81.    Then,  the  attraction 

*  In  the  Admiralty  Tide  Tables  there  are  odI^  tides  at  tea  placet  in  the 
Meditemuiean  recorded.  The  highest  spriag  tide  is  7  feet,  and  the  ave- 
rage 4*3  feet.  Admiral  Spratt,  F.R.S.»  has  just  iafomed  me  that  the 
average  of  all  spring  tides  in  the  Mediterranean  is  firom  9  to  10  inches, 
perceptible  within  three  days  of  the  highest  tide.  It  is  evident  to  me  that 
the  tide  in  that  tea  is  generated  in  hasms^  so  that  it  is  diffused  in  getting 
to  the  coast,  by  which  )  of  the  proper  height  must  be  lost. 


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Mr.  A.  Tylor  on  Tides  and  Waves.  215 

being  inversely  as  the  square  of  the  distance,  the  force  at  E  will 
be  to  that  at  W  as  31^  to  30S  or  as  961  to  900  (that  is,  one 
fifteenth  greater) .  This  calculation  ought  to  agree  with  obser- 
vation at  ports  where  the  variation  in  height  each  alternate  tide 
is  eliminated  from  other  disturbances,  and  where  there  are  no 
exceptional  circumstances,  if  this  is  a  correct  explanation  of  the 
difference  between  the  height  of  the  diurnal  and  semidiurnal 
tides  (which  1  term  the  near-side  and  far-side  tides). 

The  luni-solar  attraction-rays  in  passing  through  the  earth 
may  encounter  changes  from  fluid  to  solid  substances  having 
surfaces  not  at  right  angles  to  the  incident  ravs ;  and  the  rays 
would  not  then  follow  straight  lines,  although  I  have  for  con- 
venience represented  them  as  straight  in  fig.  4,  PI.  IV. 

Those  rays  passing  throi^rh  the  higher  parallels  of  latitude 
far  from  the  centre  might  aflfect  the  tides  apparently  in  an  irre- 
gular manner.  These  changes  of  direction  might  explain  why, 
in  order  to  predict  with  great  accuracy  the  height  and  time  of 
the  tide  at  some  stations,  Sir  W.  Thomson  and  Mr.  £.  Roberts 
have  been  obliged  to  employ  twenty-seven  fictitious  stars  instead 
of  only  the  number  to  express  the  effects  of  the  moon  and  sun's 
various  positions. 

The  different  currents  that  occur,  causing  different  establish- 
ments at  ports  near  each  other,  seem  to  indicate  movements  of 
masses  of  water  apparently  at  different  angles  to  each  other. 
These  motions  can  be  illustrated  by  an  experiment  in  the  injector. 
In  the  water-pipe,  at  right  angles  to  the  body  of  the  injector 
(where  steam  is  at  101  lbs.  pressure),  there  is  a  partial  vacuum, 
say  equal  to  2  inches  of  water.  I  find  that  the  motion  of  the 
steam  will  increase  its  own  pressure  1  lb.  by  friction  against  the 
metal  instrument.  The  steam  travelling  with  great  velocity  de- 
flects the  water-current  and  bends  it  into  its  own  direction,  and 
forces  water  into  the  steam-boiler,  where  the  pressure  is  100  lbs. 
The  water-pipe  is  all  the  time  open  to  the  atmosphere  and  to 
the  boiler  two  ways  through  the  injector;  but  little  steam 
escapes  through  the  open  water-pipe.  The  barometer  is  another 
instance.  The  column  of  mercury  ought  to  lengthen  if  that 
instrument  registered  the  absolute  weight  of  the  atmosphere 
alone,  when  the  column  of  air  is  loaded  with  vapour.  The  mo- 
tion of  the  vapour  in  the  act  of  condensing,  however,  generates 
currents  and  produces  motion  of  particles  in  a  direction  across 
the  column.  This  reduces  the  pressure  of  the  column  on  the 
cistern  of  the  barometer;  and  therefore  the  column  shortens 
for  motion  instead  of  lengthening  for  weight.  Motion  in 
main  water-pipes  reduces  pressure  in  branches  where  there  is 
no  motion. 

Currents  in  motion  in  different  directions,  owing  to  different 
temperatures  or  other  causes,  affect  the  tidal  currents  materially, 


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216  Mr.  A.  Tylor  an  Tides  and  Wooes. 

and  prevent  the  tide-gauge  ever  r^stering  the  tidal  inflaencea 
alone  at  any  point.  This  is  the  cause  of  different  establishments 
at  neighbouring  ports  apparently  in  similar  position  as  regards 
the  luni-sokr  influences. 

Fig.  1  shows  that  the  area  of  the  gap  formed  when  the  wsfe 


F.M  L//VC5  Of  HOAIZONrAL  FORWARD  MOTION    OF  PARTICLES  WITH  VERTICAL  MOTION. 

V.M  Lines  of  veat/cal  motion  of  particles  without  horizontal  motion. 

B.M  LtNES   OF  HORIZONTAL  BACKWARD   MOTION   OF  PARTICLES  WITH  VERTICAL  MOTION 

was  generated  is  the  limit  of  horizontal  movement  of  particles 
throughout  the  run  of  that  wave.  Experiments  show  that  if 
waves  artificially  produced  for  experiments  continue  the  same 
height  their  velocity  diminishes^  and  if  their  height  diminishes 
they  may  keep  up  their  velocity.  It  is  impossible  to  keep  up 
both  the  velocity  and  height  of  any  wave  a  long  distance.  If  it 
were  possible  it  would  involve  perpetual  motion,  as  the  wave  is 
resisted  by  the  air  above  and  by  the  water  in  which  it  vibrates. 
Let  t^  represent  velocity  of  the  motion  of  a  wave  measured  in 
feet  and  the  time  (a  second)  in  which  its  crest  passes  a  fixed  point, 
and  p  the  depth  of  the  water  in  feet ;  then  by  means  of  the  for- 
mula v^S^yp  the  actual  velocity  found  by  experiment  may  be 
{predicted  as  accurately  as  by  the  usual  formula  t;=\/^A^.  The 
atter  formula  appears  extremely  incorrect  for  great  depth,  as  it 
indicates  impossible  velocities  for  waves.  If  the  depth  of  the 
Atlantic  was  21,952  feet,  the  greatest  velocity  that  could  by  any 
means  be  given  to  a  wave  wouldbe  84  feet  per  second^  or  58 
miles  per  hour;  for  if  vsa\^Sp,  then  from  this  we  have 
84=8v^2l952,  that  is,  84  feet  per  second  is  the  maximum  ve- 

*  The  gravity  formula,  v*j=2gh,  only  applies  where  there  is  no  resistance 
to  motion.  It  is  of  no  use  in  cases  of  uniform  motion.  My  new  formula 
(page  205)  gives  the  due  effect  of  weight  on  velocity.  Thus  in  a  river  or 
a  glacier  with  sixty-four  times  the  quantity  (or  weight^  flowing  or  sliding, 
the  velocity  would  increase  four  times  at  the  same  slope.  "jHiis  law  ex- 
plains why  in  the  glacial  period  frozen  rivers  reached  such  low  levels,  and 
why  denudation  was  so  lar^  in  the  pluvial  period,  as  destructive  effect  is 
in  a  high  ratio  to  the  velocity. 


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Mr.  A.  Tylor  an  Tide$  and  Waves.  217 

loeity  of  the  wave,  instead  of  the  impossible  velocity  of  800  miles 
per  hoar  suggested  by  some  authors. 

An  earthquake  might  transmit  a  blow  through  the  deep  water 
in  the  ocean  at  six  miles  per  minute,  as  a  wave  was  formed  at 
Barbadoes  8000  miles  from  the  supposed  origin  of  the  shock  in 
585  minutes  after  it  was  observed  at  Lisbon.  Michelle  in  1755 
wrote  '^  when  the  bar  at  the  mouth  of  the  Tagus  was  seen  dry 
from  shore  to  shore,  then  suddenly  the  sea,  like  a  mountain,  came 
rolling  in/'  When  this  blow  struck  a  distant  coast  below  the  level 
of  the  sea,  it  would  be  reflected  and  cause  the  sea  to  ebb  from  the 
coast  first.  Then  when  the  force  which  heaped  up  the  water  away 
from  the  shore  diminished  by  work  done  upon  the  water  in  raising 
up  the  level  of  the  sea,  a  great  wave  would  be  moved  shorewards 
by  gravity.  The  first  announcement  of  the  approach  of  an 
earthquake- wave  is  the  ebb  of  the  water'*',  not  a  surface- wave. 

If  a  great  surface-wave  were  generated  by  an  earthquake,  it 
would  not  travel  veiy  far,  but  would  soon  diminish  in  height 
and  speed,  and  would  not  be  preceded  by  a  wave  in  an  opposite 
direction. 

In  some  careful  experiments  in  a  course  of  one  fifth  of  a  mile  t 
a  surface-wave  lost  five  sixths  of  its  height.  A  powerful  shock 
or  impulse  could  possibly  be  communicated  through  deep  water, 
like  a  blow  through  a  solid  body,  an  immense  distance  with 
great  velocity ;  but  that  is  not  the  case  of  a  surface-wave  at  all. 

There  is,  therefore,  a  great  distinction  between  primitive  tidal 
impulses  and  the  secondary  waves  that  accompany  or  follow 
them,  or  the  movements  in  coast-water  produced  at  distant  places 
and  times  by  means  of  the  composition  of  forces.  The  tidal  im- 
pulse is  communicated  rather  in  the  manner  motion  is  conveyed 
from  a  steam-engine  through  mechanical  gearing,  such  as  drivers 
and  followers,  and  where  there  is  lost  time  and  lost  motion  be- 
tween the  teeth  of  the  driving-wheels,  or  bands  and  pulleys,  or 
levers,  or  other  parts  of  the  apparatus  through  which  the  move- 
ment is  communicated  from  a  prime  mover  to  some  distant 
point. 

Thus  the  piston  may  have  commenced  its  down-stroke  before 
the  effect  of  the  former  up-stroke  had  reached  the  extremity  of 
the  shafting.  This  lost  motion  is  very  perceptible  in  figs.  1  and 
2,  Plate  II.,  and  fig.  1,  Plate  III. 

The  particles  of  water  may  revolve  along  their  axes ;  or  all  the 
vibrations  may  not  be  effective,  some  of  them  neutralising  others, 
and  for  a  short  time  destroying  the  impulse  of  the  central  tide- 
generating  force,  soon  to  be  renewed. 

The  hours  at  which  high  water  arrives  are  written  against  the 

♦  MicheU,  Phil.  Trans.  1766. 
t  Brit.  Assoc.  1838,  p.  465. 


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218  Mr.  A.  Tylor  on  TideM  and  Waves. 

names  of  the  towns  situated  on  the  coast  or  river-bank  in  Plates 
II.  and  III. 

In  fig.  \,  Plate  II.j  a  point  is  assumed  in  the  Atlantic  800 
miles  from  the  Land's  End,  where  the  high-  and  low-water  level 
is  assumed  to  be  invariable,  and  where  the  mass  of  the  ocean 
water  is  supposed  to  move  east  and  west  very  slowly  in  alternate 
and  opposite  directions  in  each  tide. 

When  the  flowing  tide  is  moving  a  ship  8  miles  an  hour,  there 
is  360  miles  difierence  in  distance,  and  6  hours'  time,  between 
high  water  at  Plymouth  and  Dover ;  therefore  the  lost  motion 
is  18  miles  out  <^  860,  or  5  per  cent.  The  impulse  received  at 
Plymouth  from  the  central  slowly  moving  oceanic  water  must 
have  been  transmitted  through  the  deeper  water  at  a  much 
higher  rate,  but  only  reaches  Dover  after  travelling  at  60  miles 
an  hour.  Then  the  impulse  is  transmitted  from  Dover  to  Lon- 
don at  the  rate  of  120  miles  in  three  hours,  or  40  miles  an  hour, 
the  tide  only  taking  a  ship  9  miles  in  8  hours ;  so  that  the  lost 
motion  is  9  miles  out  of  120,  or  7  per  cent.,  the  difference  of 
time  between  Plymouth  and  Dover  (21  minutes)  not  being  taken 
into  account. 

I  have  allowed  a  slope  of  1  foot  in  Plates  II.  and  III.  to  bring 
the  water  to  the  mouth  of  the  Clyde,  and  5  feet  to  bring  the  water 
to  Falmouth  from  the  Atlantic 

If  the  level  of  the  ocean  were  kept  up  above  its  due  level  only 
2  inches  between  the  western  and  eastern  boundary  of  the 
Atlantic  deep  wator^  that  slope  would  suffice  to  create  a  current 
of  8  feet  per  minute  in  the  whole  mass  of  deep  water.  This  is 
supposing  the  law  of  velocity  followed  the  ratio  I  observe  in 
smaller  cases.  If  the  two  inches  were  only  water  heaped  up  in 
consequence  of,  or  by  the  hmi-solar  attraction,  it  would  create 
no  current  at  all  while  that  attraction  continued. 

As  the  effect  of  the  moon  on  the  oceanic  water  is  only  eqoal 
to  that  of  a  sphere  of  118*75  miles  in  diameter,  equal  in  mean 
density  to  the  earth,  placed  near  and  revolving  about  C  in  a  lunar 
day,  it  occurred  to  me  that  some  geological  difficulties,  such  as 
the  evidence  in  the  Crag  and  Quaternary  deposits  of  the  tides  in 
the  Quaternary  period  being  three  or  four  times  as  large  as  at 
present,  might  be  explained  by  periodic  changes  of  position 
of  part  of  the  interior  of  the  earth,  rather  than  by  supposing 
great  changes  in  the  distance  of  the  moon  from  the  earth.  Also 
the  quantity  of  water  in  the  ocean  can  only  be  the  difference 
between  that  of  the  vapour  held  in  the  atmosphere  or  condensed 
into  snow  or  ice  on  the  land,  and  the  quantity  of  water  or  vapour 
of  water  mechanically  or  chemically  combined  with  the  strata  of 
the  earth.  These  are  Quantities  capable  of  enormous  variation  in 
geological  periods  under  different  conditions.     There  is  also  a 


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Mr.  A.  Tylor  on  Tides  and  Waves.  219 

periodicity  about  the  alternation  of  land  and  water  surfaces, 
particularly  in  the  Carboniferous  period^  which  might  be  ex- 
plained by  slow  changes  in  long  intervals  of  the  disposition  of 
the  solid  and  fluid  internal  substance  of  the  earth  with  regard 
to  and  about  its  centre. 

A  slow  circulation  of  an  eccentric  mass  of  fluid  may  occur  in 
the  interior  of  the  earth,  and  gases  may  periodically  pass  from  one 
part  of  the  solid  portion  to  another,  their  place  being  supplied 
by  fluids,  attracting  the  ocean  unequally. 

Unequal  attraction  from  variable  subterraneous  inequalities 
would  affect  different  points  of  the  surface  and  raise  the  water- 
level  on  one  part  for  long  periods  and  depress  it  on  alternate  and 
opposite  points  to  an  equal  extent.  The  theory  of  inconstancy 
of  rainfall  and  of  fluctuation  of  the  sea-level  in  ^logical  periods 
is  gaining  ground  since  I  first  advanced  these  views  (in  1858)  in 
this  Journal,  in  a  paper  entitled  ^'  Fluctuations  of  the  Sea4evel 
in  stated  Periods  of  Time." 

We  must  not  gauge  our  interpretation  of  nature  by  the  pre* 
sent  temperature,  rfonfall,  or  tide-gauges^  but  from  the  actual 
evidence  presented  in  the  strata  themselves. 

In  conclusion,  if  all  the  lines  of  Itmar  attraction  M^  M^  &c. 
(flg.  4,  PI.  IV.)  were  continued  through  the  earth  without  deflec- 
tion from  a  straight  line,  then  there  could  be  only  one  lunar  tide  ill 
the  twenty-four  hours;  for  all  the  water  on  one  side  of  the  axial 
line,  E  G  W  or  half  the  globe,  moving  in  the  direction  of  the  ro- 
tation of  the  earth,  would  be  accelerated,  and  all  the  water  in  the 
other  half,E  B  W,  of  the  globe  would  be  retarded,  a^  th^  attraction 
of  the  moon  in  that  half  would  be  contrary  to  the  direction  of  the 
rotation  of  the  earth.  The  fact  of  the  tides  occurring  ^v^ry  twelve 
hours  is  a  proof  that  the  view  J  have  put  forward  of  the  defleo* 
tion  of  the  attracting  rays  in  their  passage  through  the  earth  is 
a  correct  one.  The  twelve-hour  tides  on  the  opposite  side  of  the 
earth  to  the  moon  are  physical  proofs  that  att»*action-rays  are  de- 
flected. If  not,  there  could  be  no  such  effect  of  attraction  on  th^ 
ocean  as  is  shown  by  the  twelve-hour  tide.  The  theoretical 
differences  of  one  fifteenth  of  the  height  of  alternate  tides  I 
believe  accord  with  observation,  taking  the  average  of  the  world. 

According  to  Professor  Stokes,  any  solution  of  a  problem  that 
satisfies  all  the  conditions  must  be  the  true  one.  I  believe 
the  solution  suggested  in  this  letter  conforms  entirely  to  the* 
facts,  and  that  the  deflection-theory,  now,  I  believe,  first  pro- 
posed, is  true.  YourB  truly, 

A.  Tylor. 

P.S.  With  regard  to  the  new  equations  to  the  flow  of  water 
in  page  305, 1  use  coefficients  for  different  materials  of  channels : 
see  note  to  PI.  III.  fig.  3. 


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[    220    ] 
XXXII.  Proceedings  qf  Learned  Societies. 

ROYAL  SOCIETY. 
[Continued  from  p.  153.] 

February  6,  1874. — Joseph  Dalton  Hooker,  C.B.,  President,  in 

the  Chair. 

n^HE  following  c<Mnmunication  was  read : — 

^     **  On  a  Self-recording  Method  of  Measuring  the  Intensity  of 

the  Chemical  Action  of  Total  Daylight.**    By  H.  E.  Eosooe,  F  JI.S. 

The  object  of  the  present  communication  is  to  describe  an  instru- 
ment by  which  the  varying  intensity  of  the  chemically  active  rays, 
as  affecting  chloride  of  silver  paper  of  constant  sensitiveness,  can  be 
made  self-recording.  The  method  described  by  the  author  in  the 
Bakerian  Lecture  for  1865,  although  it  has  been  the  means  of 
bringing  into  notice  many  impor^mt  tscta  concerning  the  distribu- 
tion of  the  sun^s  chemical  activity  throughout  the  atmosphere,  as 
well  as  in  different  situations  on  the  earth's  surface,  has  not  as  yet 
been  introduced  as  a  portion  of  the  regular  work  of  meteorological 
observatories,  owing  to  ihe  hxt  that,  in  order  to  obtain  a  satis&o- 
tory  curve  of  daily  chemical  intensity,  at  least  hourly  observations 
need  to  be  made,  and  this  involves  the  expenditure  of  more  time 
and  labour  than  it  has  been  found  possible  to  give.  In  the  pre- 
sent communication  a  method  is  described,  which,  whilst  preserving 
untouched  the  principles  and  accuracy  of  the  former  method,  re- 
duces the  personal  attention  needed  for  carrying  out  the  measure- 
ments to  a  minimum,  and  thus  renders  its  adoption  in  observatories 
possible. 

According  to  this  plan,  a  constant  sensitive  paper  is  exposed  by 
a  self-acting  arrangement  for  accurately  known  times,  at  given 
intervals  throughout  the  day.  The  insolation  apparatus  stocked 
with  sensitive  paper  is  placed  in  position  either  eany  in  the  morn- 
ing of  the  day  during  which  the  measurenients  have  to  be  made,  or 
on  the  previous  night,  and  by  means  of  an  electric  communication 
with  a  properly  arranged  clock,  the  sensitive  paper  is  exposed  every 
hour  during;  the  day,  so  that,  in  the  evening,  the  observer  has  only 
to  read  off,  in  the  ordinary  manner,  the  hourly  intensities  which 
have  been  recorded  on  the  paper  during  the  day. 

This  self-recording  arrangement,  though  apparently  simple,  in- 
volves points  which  mive  rendered  its  successful  completion  a  some- 
what difficult  matter,  owing,  in  the  first  place,  to  the  great  varia- 
tions which  occur  in  the  chemical  intensity  of  total  daylight  in 
different  places,  at  different  times  of  the  day,  and  in  different  pe- 
riods of  the  year ;  and  secondly,  owing  to  the  fact  that,  in  oraer 
to  be  able  to  estimate  the  chemical  intensity,  the  coloration  ac- 

2uired  by  the  paper  must  reach,  but  not  much  exceed,  a  given  tint, 
t  becomes  necessary  therefore  that  on  each  occasion  when  an  ob- 
servation is  needed,  the  sensitive  paper  should  be  exposed  me- 


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Royal  Society.  221 

chanically,  not  once,  but  for  several  known  but  varying  intervals 
of  time  quickly  succeeding  each  other ;  so  that  whatever  may  be 
the  intensity  of  the  total  daylight  (supposed  during  these  intervals 
to  remtdn  constant),  some  one  ajb  least  of  the  several  expose^ 
papers  will  possess  the  requisite  shade.  This  is  accomplished  by 
a  duplicate  arrangement  of  a  clock  and  insolation-apparatus,  by 
means  of  which  disks  of  the  constant  sensitive  paper  are  exposed 
each  hour  for  successive  known  intervals  of  time,  varying  from  two 
to  thirty  seconds.  After  an  interval  of  an  hour,  another  set  of 
•  disks  are  exposed  for  the  same  series  of  intervals ;  and  these  series 
of  insolations  are  repeated  once  every  hour  during  the  day.  The 
mechanical  arrangements  for  effecting  this  with  accuracy  are  fully 
described  in  the  paper.  On  unrolling,  at  the  end  of  the  day,  the 
strip  of  sensitive  paper  which  has  served  for  the  exposures,  black 
disks  showing  where  the  paper  has  been  stationary  for  the  hour 
are  seen ;  and  between  each  of  these  are  found  ten  ordes  variously 
tinted,  from  that,  probably,  scarcely  visible,  which  was  exposed  for 
two  seconds,  to  that,  perhaps  too  dark  to  read  off,  which  was  inso- 
lated  for  thirty  seconds.  Amongst  these,  some  one  at  least,  will 
be  found  of  such  a  shade  as  to  enable  it  to  be  read  off  by  the  mo- 
nochromatic soda-flame,  on  a  graduated  fixed  strip,  as  described  in 
former  communications. 

A  new  method  of  calibrating  the  fixed  strips  of  standard  tints 
necessary  for  these  measurements  is  next  described ;  and  the  ques^ 
tion  as  to  the  possibility  of  preparing  constant  sensitive  paper  in 
long  strips  instead  of  in  large  sheets  is  next  experimental^  dis- 
cussed, the  result  of  the  examination  being  that  it  is  possible  to 
prepare  silvered  paper  in  long  narrow  strips  such  as  are  used  in 
Morse's  tel^raph-apparatus,  so  that  it  shaU  throughout  its  length 
preserve  the  standard  sensitiveness. 

The  time  during  which  the  disks  of  constant  sensitive  paper  are 
exposed  is  next  ascertained  for  each  instrument  by  a  chronc^raph. 

During  wet  weather  the  insolator  is  covered  by  a  semicircular 
glass  shade ;  and  the  value  of  the  coefficients  for  refraction  and 
absorption  due  to- this  glass  shade  is  determined. 

The  latter  portion  of  the  communication  contains  the  results  of  a 
deries  of  comparisons  of  the  curves  of  daily  chemical  intensity  ob- 
tained (1)  with  the  hand-insolator,  and  (2)  with  the  self-recording 
instrument.  Comparisons  of  this  nature  were  made  during  the 
months  of  May,  June,  and  July,  1873,  by  simultaneous  hourly  de^ 
terminations  in  the  neighbourhood  of  Manchester  according  to  both 
methods.  Of  these  observations,  six  full  days  are  selected  ;  and  the 
tables  and  curves  accompanying  the  communication  show  the  close 
correspondence  of  both  sets  of  observations.  The  integrals  of  total 
chemical  intensity  for  these  days  are  also  given,  and  exhibit  as  close 
an  agreement  as,  from  the  nature  of  the  experiments,  can  be  ex- 
pected. 


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222  Rnyal  SoeUty  :— 

Feb.  12. — Joseph  Dalton  Hooker,  C.B.,  President,  in  the  Chair. 

The  following  communication  was  read : — 

"  On  the  Division  of  a  Sound- Wave  by  a  Layer  of  Flame  or  heated 
Gas  into  a  reflected  and  a  transmitted  Wave."  By  John  Cottrell, 
Assistant  in  the  Physical  Laboratory  of  the  Royal  Institution. 

The  incompetency  of  a  sound-pulse  to  pass  through  non-homo- 
geneous air  having  been  experimentally  demonstrated  by  Dr.  Tyn- 
daU,  and  proved  to  be  due  to  its  successive  partial  reflections  at  the 
limiting  surfaces  of  layers  of  air  or  vapour  of  different  density, 
further  experiments  were  conducted  in  order  to  render  visible  the ' 
action  of  the  reflected  sound-wave. 

The  most  successful  of  the  various  methods  contrived  for  this 
purpose  consists  of  the  following  arrangement.  A  vibrating  bell 
contained  in  a  padded  box  was  directed  so  as  to  send  a  sound- 
wave through  a  tin  tube,  B  A  (38  inches  long,  1 1  inch  diameter), 
in  the  direction  BF,  its  action  being  rendered  manifest  by  its 
causing  a  sensitive  flame  placed  at  F*  to  become  \iolently  agitated. 

The  invisible  heated  layer  immediately  above  the  luminous  por- 
tion of  an  ignited  coal-gas  flame  issuing  from  an  ordinair  bat's- 
wing  burner  was  allow^  to  stream  upwards  across  the  end  of  the 
tin  tube  B  A  at  A.  A  portion  of  the  sound-wave  issuing  from  the 
tube  was  reflected  at  the  limiting  surfaces  of  the  heat«d  layer ; 
and  a  part  being  transmitt-ed  through  it,  was  now  only  competent 
to  slightly  agitate  the  sensitive  flame  at  F. 


The  heated  layer  was  then  placed  at  such  an  angle  that  the  re- 
flected portion  of  the  sound-wave  was  sent  through  a  second  tin 
tube,  A  F  (of  the  same  dimensions  as  B  A),  its  action  being  ren- 
dered visible  by  its  causing  a  second  sensitive  flame  plaodd  at  the 
end  of  the  tube  at  F  to  become  violraitly  i^ected.  This  action 
continued  so  long  as  the  heated  layer  intervened;  but  upon  ite 
withdrawal  the  sensitive  flame  placed  at  F,  receiving  the  whole  of 
the  direct  pulse,  became  again  violently  agitated,  and  at  the  same 
moment  the  sensitive  flame  at  F,  ceasmg  to  be  affected,  resumed 
it«  former  tranquillity. 

Exactly  the  same  action  takes  place  when  the  luminous  portion 
of  a  gas-flame  is  made  the  reflecting  layer ;  but  in  the  experimente 
above  described,  the  invisible  layer  above  the  flame  only  was  used. 
By  proper  adjustment  of  the  pressure  of  the  gas,  the  flame  at  F 
can.  be  rendered  so  moderately  sensitive  to  the  direct  sound-wave. 


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Mr.  Donkin  on  the  Contrition  of  two  Harmonie  Curves.    223 

that  the  portion  transmitted  through  the  reflecting  layer  shtAi  be 
incompetent  to  affect  the  flame.  Then  by  the  introduction  and 
withdrawal  of  the  batVwing  flame  the  two  sensitive  flames  can  be 
rendered  alternately  quiescent  and  strongly  agitated. 

An  illustration  is  here  afforded  of  the  peif ect  analogy  between 
light  and  sound ;  for  if  a  beam  of  light  be  projected  from  B  to  F", 
and  a  plate  of  glass  be  introduced  at  A,  in  the  exact  position  of  the 
reflecting  layer  of  gas,  the  beam  will  be  divided,  and  one  portion 
will  be  reflected  in  the  direction  A  F,  and  the  other  portion  trans- 
mitted through  the  glass  in  the  direction  F*,  exactly  as  the  sound- 
wave is  divided  into  a  reflected  and  a  transmitted  portion  by  the  layer 
of  heated  gas  or  flame. 

Feb.  19. — Joseph  Dalton  Hooker,  C.B.,  President,  in  the  Chair. 

The  following  communication  was  read : — 

'*  On  an  Instrument  for  the  CompoBiticm  of  two  Harmonic 
Curves.''  By  A.  E.  Donkin,  MA.,  F.iLa.S.,  Fellow  of  Exeter  Col- 
l^;e,  Oxford. 

The  interest  in  such  compound  curves  lies  in  the  fact  that,  as  a 
simple  harmonic  curve  may  be  considered  to  be  the  curve  of  pres^ 
sure  on  the  tympanic  membrane  when  the  ear  is  in  the  nei^bour*- 
hood  of  a  vibrating  body  producing  a  simple  tone,  so  a  curve  com- 
pounded of  two  such  simple  harmonic  curves  will  be  the  carve  of 
pressure  for  the  consonance  of  the  two  tones  which  they  severally 
represent,  and  thus  the  effect  on  the  ear  of  different  oonsonances 
can  be  distinctly  represented  to  the  eye. 

If  the  motion  of  a  point  be  compounded  of  rectilinear  harmonic 
vibrations  and  of  uniform  motion  m  a  straight  line  at  right  angles 
to  the  direction  of  those  vibrations,  the  point  will  describe  a  simple 
harmonic  curve. 

Thus  a  pencil-point  performing  such  vibrations  upon  a  sheet  of 
paper  moving  umformly  at  right  angles  to  Hkeir  direction  would 
oraw  such  a  curve. 

The  same  kind  of  curve  would  also  be  drawn  by  keeping  the 
pencil  fixed  and  by  giving  to  the  paper,  in  addition  to  its  continuous 
transverse  motion,  a  vibratonr  motion  similar  and  parallel  to  that 
whidi  the  pencil  had ;  and  ii  ihe  motion  of  the  latter  be  ndw  re^ 
stored,  a  complicated  curve  will  be  produced  whose  f  onn  will  depend 
on  the  ratio  of  the  numbers  of  vibrations  in  a  given  time  or  the 
pencil  and  paper,  and  which  will  be  the  curve  m  pressure  for  the 
interval  corresponding  to  this  ratio. 

The  manner  in  which  these  three  motions  are  combined  in  the 
machine  is  as  follows : — ^Two  vertical  spindles,  A  and  B,  revolving 
in  a  horizontal  plate  carry  at  their  lower  ends  each  a  crank,  0  and 
D,  and  at  their  upper  ends  each  a  wheel  cut  with  a  certain  number 
of  teeth ;  these  two  wheels  can  be  connected  by  means  of  an  inter- 
mediate one,  as  is  seen  in  the  figure ;  and  since  either  wheel  of  the 
pair  can  be  replaced  by  another  with  a  different  number  of  teeth,  the 
relative  angular  velocities  of  the  spindles  can  be  regulated  at  plea- 
sure. The  paper  upon  which  the  curve  is  to  be  drawn  is  carried  upon 


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224    Roifal  Society :—  Mr.  A.  E.  Donkin  on  an  Instrument 

a  rectangukr  frame,  E  F  G  H,  capable  of  sUding  boriax)ntally  up  and 
down  in  a  direction  parallel  to  that  of  the  plane  passing  througli  the 


spindles.  This  frame  has  a  pair  of  rollers,  E  F  and  G  H  at  eax^b  end 
connected  by  tape  bands,  between  which  the  paper  passes  as  t^^  ^^' 
lers  turn.  In  order  to  give  a  motion  of  reyoiution  to  the  roH^^^'  * 
wheel,  L,  is  fixed  upon  the  axis  of  one  of  them  whose  teet>li  Sl^ 


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for  the  Composition  of  two  Harmonic  Curves.  225 

into  those  of  a  pinion,  P  Q,  alongside  which  the  frame  slides,  and 
which  is  itself  driven  by  one  of  the  vertical  spindles.  A  connecting- 
rod,  D  M,  is  carried  to  the  frwne  from  the  crank  of  this  spindle,  so 
that  upon  turning  the  latter  a  vibratory  motion  is  given  to  the 
former ;  and  since  the  transverse  motion  of  the  paper  aJso  d^jends 
upon  the  same  spindle,  a  fixed  pencil-point  resting  on  it  would 
draw  a  simple  harmonic  curve  whose  amplitude  would  depend  on 
the  radius  of  the  crank,  and  wave-length  on  the  transverse  speed  of 
the  paper,  which  can  be  regulated  at  pleasure  by  means  conj^ived 
for  the  purpose*. 

A  vibratory  motion  similar  and  parallel  to  that  of  the  frame  is 
^ven  to  a  small  tubular  glass  pen,  E,  so  arranged  as  to  move  with 
its  point  lightly  resting  upon  the  paper.  This  motion  is  commu- 
nicated by  a  connecting-rod,  C  N,  from  the  other  crank,  which  is 
carried  underneath  the  sliding  frame  and  jointed  to  the  lower  end 
of  a  small  vertical  lever,  S,  to  whose  upper  end  the  arm  carrying 
the  pen  is  attached. 

The  weight  W  serves  to  regulate  the  pressure  of  the  pen  on  the 
paper,  as  it  can  be  screwed  in  or  out.  T  is  merely  a  pillar  upon 
wluch  the  change-wheels  can  be  placed  for  convenience. 

If  the  pair  of  wheels  on  the  spindles  are  now  connected  by  the 
intermediiftte  one,  it  is  plain  that,  upon  turning  either  of  the  spin- 
dles by  a  winch  provided  for  the  purpose,  the  two  motions  of  the 
paper  will  be  combined  with  that  of  the  pen,  and  the  curve  drawn 
will  be  that  composed  of  the  two  simple  harmonic  ones  which 
would  be  the  result  of  separately  combining  the  harmonic  vibrations 
due  to  each  crank  with  the  transverse  motion  of  the  paper.  Thus,  if 
m  and  n  are  the  numbers  of  teeth  on  the  pair  of  wheels  respectively, 
the  equation  to  the  resultant  curve  will  be 

y=sin  ww7-f  sin  nx. 

This  equation  implies  not  only  that  the  radii  of  the  cranks  are  the 
stune,  but  also  that  they  start  parallel  to  each  other  and  at  right 
angles  to  the  vertical  plane  passing  through  their  axes :  both  these 
conditions  can,  however,  be  altered ;  and  therefore  the  general  form 
of  equation  to  the  curves  which  the  machine  can  draw  will  be 

y=a  sin  (ww?-fa)-f6  siu  (wa?  +  /3), 
where  a  and  h  are  the  radii  of  the  cranks,  and  a  and  ^  are  depen- 
dent on  their  relative  inclinations  to  the  above-mentioned  vertical 
plane  at  starting. 

As  an  example,  suppose  that  a =6,  while  the  ratio  of  m  to  n  is  as 
2  to  1 ;  then  the  above  equation  will  represent  the  curve  of  pressure 
for  the  octave.     Similarly,  ifmistonasl6  to  15,  the  resultant 

*  It  BhouM  be  observed  here  that  the  vibratory  motion  thus  given  to  the  fVame 
is  not  truly  barmonic.  In  order  to  make  it  so,  a  more  complicated  contrivance 
tban  the  simple  crank  and  connecting-rod  would  bave  to  ue  adopted ;  but  this 
would  probably  introduce,  through  unavoidable  play,  an  error  greater  than  the 
present  one,  the  length  of  the  connecting-rods  and  Uie  small  size  of  the  cranks 
rendering  the  latter  nearly  inappreciable.  The  motion  will,  however,  for  the  sake 
of  convenience,  be  considered  truly  harmonic  throughout 

Phil  Mag.  S.  4.  Vol.  4«.  No.  317.  Sept.  1874.  Q 


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226  Royal  Society. 

curve  represents  the  effect  on  the  ear  of  a  diat<Hiic  semitone,  while 
the  ratio  81  to  80  would  give  that  of  the  comma.  In  hoth  these 
curves,  and  more  especially  in  the  latter,  the  beats  which  would 
ensue  on  actually  sounding  the  two  tones  together  are  shown  with 
lemarkable  distinctness. 

As  the  machine  is  provided  with  a  set  of  change-wheels,  many 
different  curves  can  be  produced,  while  ihe  form  of  leach  can  be 
more  or  less  changed  by  altering  the  relative  positions  of  the 
cranks  before  bringing  the  idle  wheel  into  gear.  It  is  also  possible 
to  obtain  very  large  values  of  m  and  n  in  the  above  equation  by 
using  two  idle  wheels  on  the  same  axis,  which  shall  come  into  gear, 
the  upper  one  with  the  wheel  on  the  one  spindle,  the  lower  one  with 
that  on  the  other. 

Thus,  suppose  A  and  B  are  the  numbers  of  teeth  on  the  spindle- 
wheels  respectively,  C  and  D  those  on  the  idle  wheels,  ana  let  A 

BC 

gear  with  C  and  D  with  B ;  then  —  s  -r^ .     Now,  by  properly 

n       AD 

choosing  the  four  wheels,  large  values  of  m  and  n  may  be  obtained. 

If,  for  instance,  A=81,  B=80,  C=55,  and  D-27,  -  =^^ ;  this 

n      2187 

2 
ratio  being  nearly  =  -,  the  corresponding  curve  will  represent  the 

effect  of  an  octave  slightly  out  of  tune.  The  period  of  such  curves 
as  these  being  very  long,  it  is  necessary  to  have  a  good  supply  of 
paper ;  and  this  is  arranged  by  carrying  a  reelf  ul  on  the  horizontal 
frame,  from  which  it  is  slowly  unwound  between  the  rollers.  The 
rate  at  which  this  takes  place  has  a  good  deal  of  influence  on  the 
form  of  the  resultant  curve ;  the  slower  it  is,  the  more  compressed 
will  the  latter  appear.  Instead  of  using  paper,  the  curves,  pro- 
vided the  periods  are  short  enough,  may  be  drawn  on  slips  of  black- 
ened glass,  which  can  be  carried  along  between  the  tapes  connecting 
the  rollers ;  they  can  be  at  once  pUced  in  a  lantern  and  thrown  on 
a  screen. 

The  width  of  contour  of  any  curve  depends  on  the  radii  of  the 
cranks :  these  may  have  any  value  between  0  and  half  an  inch ;  and 
therefore  the  limit  of  possible  width  at  any  part  will  be  two  inches ; 
so  also,  by  altering  the  radii,  a  series  of  curves  may  be  produced 
corresponding  to  the  consonances  of  tones  not  of  the  same  inten- 
sities. Since  the  maximum  width  of  any  curve  will  be  double  the 
sum  of  the  radii  of  the  cranks,  the  paper  is  cut  to  a  width  of  two 
and  a  half  inches,  within  which  all  curves  which  can  possibly  be 
drawn  will  be  comprised. 

The  instrument  is  constructed  by  Messrs.  Tisley  and  SpiDer,  of 
Brompton  £oad,  to  whom  some  improvement  upon  the  original 
model  it  due. 


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Geological  Society.  227 

QEOLOOICAL  SOCIETY. 

[Continued  from  p.  155.] 

November  19,  1873.— Prof.  Ramsay,  F.R.S.,  Vice-President, 
in  the  Chair. 

The  following  commnnications  were  read : — 

1.  **  Supplemental  Note  on  the  Anatomy  of  HypsHaphodon 
Foxii:'    By  J.  W.  Hulke,  Esq.,  P.E.S.,  P.G.S. 

The  material  for  this  note  was  a  slab  from  Cowleaze  Chine,  oon- 
taining  portions  of  two  indiyidoals  of  HypsUophodon  Foxii—one  con* 
sisting  of  a  skull  with  a  great  part  of  the  vertebral  column,  the 
other  of  a  portion  of  the  vertebial  column.  The  author  described 
some  details  of  the  structure  of  the  skuU,  and  especially  the  palatal 
apparatus.  The  pterygoids,  which  are  not  mesially  joined,  have  a 
stout  body,  the  posterior  border  of  which  bears  a  very  large  basi- 
sphenoidal  process ;  and  the  left  pterygoid  retains  the  root  of  a  strong 
quadratic  process,  in  front  of  which  the  hollow  outer  b<Nrder  runs  out 
into  an  ectopterygoid.  In  front  of  the  pterygoids  the  palatines  are 
partially  visible,  also  separated  by  a  fissure.  Of  the  eight  vertebrae, 
the  last  three  are  firmly  anchylosed,  and  the  seventh  and  eighth 
form  part  of  the  sacrum.  They  are  constricted  in  the  middle ; 
and  their  transverse  processes,  which  spring  from  the  junction  of 
two  vertebrsB,  are  bent  backwards,  joiniog  the  dilated  outer  end  of 
the  trausverse  processes  of  the  next  vertebra,  including  a  laige  sub- 
circular  loop.  The  second  fragment  of  a  vertebral  column,  which 
belonged  to  a  smaller  individual,  includes  the  sacrum  and  several 
vertebrcB.  Near  the  skull  the  slab  contains  several  very  thin  bony 
plates  of  irregularly  polygonal  form,  regarded  by  the  author  as 
dermal  scutes.  In  connexion  with  the  question  of  the  generic  rank 
of  Hypsilophodon^  the  author  stated  that  in  Hyp9ihphod(m  the 
centra  of  the  sacral  vertebrae  are  cylindroid  and  rounded  below, 
whilst  in  Iguanodon  they  are  compressed  laterally  and  angulated 
below. 

2.  "  The  Drift-beds  of  the  North-west  of  England.— Part  1,  Shells 
of  the  Lancashire  and  Cheshire  Low-level  Clay  and  Sands."  By  T. 
Mellard  Eeade,  Esq.,  C.E.,  F.G.8. 

The  author  commenced  by  explaining  a  section  in  a  cutting  at 
Booth-Lane  Station,  in  which  most  of  the  beds  seen  about  Liverpool 
are  typically  represented.  This  section  shows  in  ascending  order : — 
1.  Pebble-beds  of  the  Trias  ;  2.  shattered  rock.;  3.  compacted 
red-sand  rubWe  (ground  moraine) ;  4.  lowest  bed  of  Boulder-clay 
(largely  composed  of  red  sand);  5.  stratified  sand,  with  shell- 
fragments  ;  6.  bed  of  fine  unctuous  clay  ;  7.  brick-clay  (with  many 
shells) ;  8.  sand-bed ;  9.  stratified  yellow  sand  ("  Washed  Drift 
sand"). 

The  author  next  gave  a  list  of  the  loealities  in  which  shells  were 
found,  and  stated  that  in  all  forty-six  species  had  been  met  with 
distributed  through  the  day-beds,  those  found  in  the  sand-seams 
being  rare  and  generally  frtigmentary  and  rolled.    The  shells  mobt 

Q2 


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228  Geological  Socieiy  :— 

commonly  found  entire  are  usuallj  of  small  tjiize,  and  of  a  form  cal- 
culated to  resist  pressure, — such  as  TurriteUa  communis,  Trophon 
daihratus,  and  Mangelia  turricula,  Pusus  antiqutM  and  Buccinum 
undatum  are  generally  represented  only  by  worn  fragments  of  the 
columella;  and  Cyprina  islandica  is  always  found  in  fragments. 
The  author  thought  that  the  association  of  the  various  species  dis- 
tributed without  order  through  the  clays  shows  that  they  could  not 
have  lived  together  on  the  same  bottom,  but  that  they  must  have 
been  to  a  great  extent  transported.  He  contended  that  the  ad- 
mixture of  shells  in  the  Boulder-clay  was  due  to  tbe  tendency  of  the 
sea  to  throw  up  its  contents  on  the  beach,  whence  changing  cur- 
rents and  floating  ice  might  again  remove  them,  and  to  the  oscilla- 
tions of  the  land  bringing  all  the  beds  at  one  time  or  another  within 
reach  of  marine  erosive  action.  He  maintained  that  it  is  in  the 
distribution  of  land  and  sea  at  the  period  of  deposition  of  the  Lan- 
cashire deposits,  and  not  in  astronomical  causes,  that  we  must  seek 
the  explanation  of  the  climate  of  that  period,  the  conditions  of  which 
he  endeavoured  to  explain  by  a  consideration  of  the  proportions  of 
the  species  and  the  natural  habitats  of  the  shells  found  in  the  drifts. 

3.  "  Note  on  a  deposit  of  Middle  Pleistocene  Gravel  near  Ley- 
land,  Lancashire."     By  R.  D.  Darbishire,  Esq,,  F.G.8. 

The  bed  of  gravel,  about  40  feet  thick,  and  about  240  feet  above 
the  level  of  the  sea,  is  covered  by  yellow  brick  clay,  and  overlies  an 
untried  bed  of  fine  sea-sand.  The  shells  dhd  fragmens  occur  chiefly 
at  the  base  of  the  gravel. 

The  most  noticeable  shells  in  this  list  of  forty-two  species,  col- 
lected by  Miss  M.  H.  Farington,  were  Panopoea  norvegica,  Macira 
glauca,  Cyiherea  chione,  Cardium  rusticum,  Fusus  propinquuB,  and 
Fusus  antiqutts,  var.  contrarius.  One  specimen  of  a  Fmus,  doubt- 
fully identified  as  F.  Fabricii  (craticulatus),  had  occurred. 

The  group  was  by  no  means  characteristically  Arctic  or  Glacial. 
It  represented  most  nearly  the  Wexford  lists,  especially  in  present- 
ing the  reversed  Fusus,  and  might  be  regarded  as  connecting  those 
beds  with  the  Macclesfield  drifts,  also  containing  a  Celtic  assortment, 
with  Cytherea  chimie  and  Cardium  rusticum. 

The  author  considered  the  Leyland  deposit,  like  those  on  the  west 
of  the  Derbyshire  hills,  to  be  more  probably  littoral  and  truly  cli- 
matic than  that  of  the  Liverpool  clays,  the  subject  of  Mr.  Keade's 
Paper,  and  hazarded  the  conjecture  that  the  latter  were  sea-bottom 
beds,  into  which,  during  some  process  of  degradation  and  redistri- 
bution, the  specimens  found  and  enumerated  by  Mr.  Keade  had  been 
carried  down  from  the  former  more  ancient  retreating  coast-lines. 

December  3rd,  1873.— Joseph  Prestwich,  Esq.,  F.R.8., 
Vice-President,  in  the  Chair. 

The  following  communications  were  read : — 
1.  '*  Notes  on  the  Structure  sometimes  developed  in  Chalk.''     By 
H.  George  Fordham,  Esq.,  F.G.S. 

After  referring  to  Mr.  Mortimer's  paper  on  tbe  same  subject  (see 


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Mr.  R.  PiDchin  on  the  Geologg  of  the  Cape  of  Good  Hope.    299 

Q.  J.  G.  8.  vol.  xxix.  p.  417),  the  author  stated  that  in  a  pit  near  Ash- 
well  the  **  Lower  Chalk  without  flints  *'  exhibits  a  bed  of  a  concre- 
tionary nature,  the  concretions  in  which  are  marked  nearly  all  over 
with  lines.  The  lines  are  found  only  on  the  concretions  and  in  their 
immediate  neighbourhood.  The  fossils  in  the  bed  are  invariably 
crushed,  as  if  by  pressure.  The  author  believes  that  the  strisB  are 
due  to  an  incipient  crystallization  arising  from  the  formation  of  the 
concretions ;  and  in  support  of  this  view  he  adduced  a  specimen  of 
iron  pyrites  from  the  chalk  of  Beachy  Head,  attached  to  which  is  a 
small  portion  of  very  hard  striated  chalk,  and  suggested  that  the 
crystallization  of  the  pyrites  had  induced  a  crystallization  in  the  chalk. 
He  considers,  however,  that  in  some  places  an  almost  identical 
structure  may  be  due  to  slickensides,  but  only  in  very  broken  and 
faulted  beds. 

2.  "  A  short  description  of  the  Geology  of  the  Eastern  Province 
of  the  Colony  of  the  Cape  of  Good  Hope."  By  R.  Pinchin,  Esq., 
C.E.     Communicated  by  H.  W.  Bristow,  Esq.,  F.R.S.,  F.G.S. 

In  this  paper,  which  was  illustrated  by  maps  and  sections,  the 
author  gave  the  results  of  his  observations  on  the  geology  of  the 
above  region.  The  two  principal  sections  described  were  fiim  Cape 
Saint  Francis,  across  the  Great  Winterhoek  and  Langeberg  ranges,  to 
the  lacustrine  Triassic  rocks  near  Jansenville,  and  from  Port  Eliza- 
beth to  Somerset.  The  lowest  rock  in  the  first  section  is  the  quartzite 
of  the  Great  Winterhoek,  which  is  immediately  overlain  to  the 
northward  by  day-shales  and  sandstones  containing  Devonian  fossils. 
Beds  with  similar  fossils  occur  at  the  Eromme  river,  Cape  St. 
Francis,  and  near  Uitenhage.  A  patch  of  horizontal  secondary 
strata  stretches  west  from  the  Gamtoos  river,  overlying  the  Enon 
conglomerate  in  the  same  way  as  the  Jurassic  strata  of  Uitenhage. 
They  contain  no  fossils.  The  Enon  conglomerate  is  seen  on  the 
flanks  of  the  higher  hills.  The  northern  ranges,  Langeberg,  Elein 
Winterhoek,  and  Zuurbergen,  are  regarded  by  the  author  as  formed 
of  rocks  belonging  to  the  Carboniferous  series,  although  closely 
resembling  those  of  the  Great  Winterhoek  in  lithological  character, 
except  that  among  them  are  bands  of  the  peculiar  rock  described  by 
Bain  as  "  Claystone  porphyry,"  by  Wyley  as  a  **  Trap  conglomerate,'* 
by  Tate  as  a  "  Trap-breccia,"  and  by  Atherstone  as  an  "  intrusive 
Trap."  Eubidge  regarded  it  as  a  metamorphic  rock ;  and  this  view 
is  adopted  by  the  author,  who  describes  it  as  underlying  and  over- 
lying the  clay-shales,  which  always  separate  it  from  the  quartzite, 
and  as  passing  imperceptibly  into  the  clay-shales.  The  mottled 
sandstone  or  Ecca  rock  is  referred  by  the  author  to  the  Carboni- 
ferous series.  The  author  also  noticed  the  occurrence  of  Tertiary 
or  recent  rocks  containing  remains  of  Mollusca  identical  with 
species  now  living  in  the  adjacent  seas,  lying  unconformably  upon 
the  Devonian,  and  conformably  upon  the  Secondary  rocks  at  various 
places  near  the  coast. 


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230  Geological  Society. 

S.  '*  On  the  Mad-craters  and  geological  structore  of  the  Mekran 
Co^."  By  lient.  A.  W.  Stiffe,  F.R.A.S.  Communicated  by  Prof. 
Ramsay,  F.R.8.,  V.P.G.S. 

The  coast  of  Mekran,  extending  from  near  the  western  frontier  of 
India  to  the  month  of  the  Persian  Gulf,  was  stated  by  the  author  to 
be  a  nearly  rainless  district,  consbting  of  clay  plains  with  pre- 
cipitous tabular  hills,  the  former  veined  here  and  there  with  crystal- 
line gypsum,  the  latter  composed  of  clay  capped  and  sometimes 
interstiutified  with  coarse,  friable,  fossiliferous  calcareous  strata, 
from  5  to  30  feet  thick,  supposed  to  be  of  Miocene  age,  and  all 
horizontal  or  nearly  so,  except  at  the  extreme  east  and  west,  where 
the  strata  are  inclined  at  an  angle  of  frt>m  40^  to  60^.  Along  the 
coast  there  are  no  distinct  traces  of  volcanic  action;  but  on  the 
north  coast  of  the  Persian  Gidf  a  similar  formation  has  been  much 
disturbed  by  the  protrusion  of  recent  volcanic  material,  near  J&shak 
to  the  west  there  is  a  hot  mineral  spring,  and  near  Ear&chi  there 
are  springs  of  pure  hot  water.  The  author  described  the  mode  in 
which  denudation  is  effected  in  this  region  by  occasional  heavy 
rains,  and  by  the  constant  action  of  the  sea  upon  the  coast,  and  then 
noticed  the  occurrence,  within  a  few  miles  of  the  shore,  of  numerous 
peculiar  mud-craters,  forming  hills  varying  in  height  fr^m  20  to 
300  or  400  feet  above  the  plain,  of  a  regular  conical  form,  with 
truncated  tops,  and  the  sides  sloping  at  an  angle  of  about  40^.  The 
summits  of  these  hills  present  a  circular  cup  with  a  narrow  border, 
filled  with  semifluid  mud,  which  occasionally  flows  slowly  over  the 
margin  of  the  crater.  The  author  considered  that  the  conical  hills 
have  been  formed  solely  by  these  overflows.  He  believed  that  a 
small  shoal  occurring  off  the  coast  near  Jdshak  might  be  produced 
by  one  of  these  craters,  and  was  inclined  to  ascribe  their  existence 
to  hydrostatic  pressure  rather  than  to  volcanic  action,  especially  as 
by  tiie  concurrent  testimony  of  several  natives  the  discharge  from 
the  craters  b  greater  during  spring  tides.  The  thickness  of  the 
clay  forming  the  plain  is  probably  very  considerable  ;  it  extends  for 
some  miles  from  the  shore,  sinking  gradually  to  20  or  30  fathoms, 
when  there  b  a 'sudden  and  often  precipit<>us  descent  to  a  depth 
of  300  or  400  fathoms.  The  author  suggested  that,  since  the  de- 
position of  the  Miocene  beds,  the  great  submarine  cliff  may  have 
been  raised  above  the  sea,  that  the  land  was  then  depressed  to  near 
its  present  level,  causing  the  removal  of  the  beds  to  the  present 
coast  Hue,  and  that  a  farther  depression  followed  by  upheaval  gave 
origin  to  the  inland  cliffs.  Evidence  of  the  last  depression  is  frir- 
nbhed  by  the  presence  of  borings  of  lithodomous  mollusca  in  the 
clifls  considerably  above  the  present  sea-leveL 


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[    231     ] 
XXXIII.  Inteliigence  and  Miscellaneous  Articles. 

ON  THB  LIGHT  RBFLKCTED  BY  PERMANGANATE  OF  POTASSIUM. 
BY  DR.  EILHARD  WIEDEMANN. 

PROFESSOE  STOKES*  observed  that  in  the  spectrum  of  the 
light  reflected  from  solid  permanganate  of  potassium  dark 
streaks  oecur^  and  that  they  are  exhibited  most  distinctlj  with  a 
certain  angle  of  inetdenee ;  further,  the  minima  of  brightness  in  i^e 
speetnim  of  the  reflected  light  correspond  to  the  rays  transmitted 
in  the  greatest  intensity  by  the  permanganate. 

I  have  pursued  this  subject  further,  and  examined  not  only  the 
lijght  reflected  at  the  boundary  of  permanganate  of  potassium  and 
air,  but  also  that  at  ihe  boundary  of  benzine,  sulphide  of  carbon, 
and  a  mixture  of  these  two  substances,  and  the  above  salt.  More- 
over the  polarizotioii  of  the  inddent  light  wa&  kept  in  view.  To 
obtain  the  reflecting  surfaces,  triturated  crystals  of  the  salt  were 
polished  upon  ground  glass  plates  by  means  of  a  jet-burnisher. 
Clean  surfaces,  free  from  oxide,  were  thereby  secured  for  the  inves- 
tigation, which  is  not  the  case  when  whole  crystals  are  employed. 
The  glass  plate  thus  prepared  was  inserted  in  a  rectangular  hollow 
prism  (which  could  be  filled  with  the  different  liquids)  in  such  wise 
that  its  coated  face  was  turned  to  the  rectftngnlar  edge.  The  pridm 
was  placed  upon  a  graduated  circular  table  that  could  be  rotated, 
and  sunlight  so  thrown  upon  one  of  the  two  surfaces  including  the 
right  angle  that  the  light  refracted  there  fell  upon  the  coated  plate 
and,  through  reflection,  passed  out  at  the  other  surface.  Thence  it 
arrived  at  the  sHt  of  a  spectrum-apparatus.  The  angle  of  incidence 
on  the  coated  plate  was  determined  thus :  the  Mght  from  the  first 
surfaee  of  the  prism  was  reflected  back  in  its  own  direction ;  the 
position  of  the  table  was  then  read  oSt ;  the  rotation  of  the  table 
with  the  prism  ^es  immediately  the  incidence- angle  at  the  first 
surfaee ;  from  this  angle  and  that  between  the  glass  plate  and  the 
first  face  of  the  prism,  and  the  index  of  refraction  of  the  medium 
i!n  contact  with  ttie  permanganate,  the  incidence-angle  at  the  latter 
can  then  be  found. 

The  position  of  the  streaks  in  the  specttuM  was  determined  by 
means  of  a  photographed  scale  applied  to  the  spectmm-apparatus, 
the  cross^threads  of  the  observing-telescope  having  previously  been 
placed  on  the  centre  of  tho  dark  streak. 

These  positions  with  pretty  large  angles  of  incidence  are  given 
in  Table  I.  The  columns  ifi^r  A  refer  to  the  streaks  in  the  light 
polarized  parallel  to  the  plane  of  incidence,  those  under  B  to  thos6 
in  the  light  polarized  perpendicular  to  that  plane.  The  first  cohnmi 
gives  the  names  of  ^e  surrounding  media.  Table  II.  gives  the 
positions  of  the  absorption-streaks  in  the  transmitted  light.  Eraun- 
hofer's  lines  correspond  as  follows  to  the  strokes  on  the  photo- 
graphed scale : — 

D:*=Oj  B=il8;  b^21',  F=«33. 

♦  Phil.  Mag.  1863,  vo!.  vi.  p.  393.     Pogg".  Ann,  1854,  vol.  xci.  p.  300. 


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232  Intelligence  and  Miscellaneous  Articles. 

Tabm  I. 


A. 

Air   

1 

14 
15 

16 

S9 

28i 
30 

3U 
82 

87  ; 

38i  1  45 
894  1  47 

Benzine   

Mixture  of  benzine  tnd  sulphide  of  carbon. 
Snlnhide  of  eftrhon 

!          -    1              1 

B. 

Air      

4 
8i 

m 
m 
m 

u 

IS 

82    38| 
82    38 
82    39 
82|89i 

S' 

Benzine 

Mixture  of  benzine  and  sulphide  of  carbon. 
Sulohide  of  carbon    

Tabls  II. 

4},     Hi,     18J,     26i,    33^. 

These  numbers  show : — 

1.  That,  with  large  angles  of  incidence,  the  streaks  in  the  light 
polarized  perpendicular  to  the  incidence-plane,  with  respect  to  those 
in  the  light  polarized  parallel  to  the  plane  of  incidence,  are  displaced 
towards  the  olue,  and  that  in  the  former  another  streak  occurs  in 
the  yicinity  of  D. 

2.  That  with  the  increase  of  the  refraction-index  of  the  surround- 
ing medium  the  streaks  in  the  parallel-polarized  light  undergo  dis- 
placements towards  the  blue ;  while,  on  the  contrary,  in  the  per- 
pendicularly-polarized light  the  streaks  preserve  their  position  un- 
changed, or  lilter  it  but  Httle.  Observation  of  the  streaks  in  the 
blue  beyond  E  is  attended  with  great  difficulties,  as  is  the  entire 
investigation,  through  the  breadth  of  the  streaks  and  the  impossi- 
bility of  obtaining  perfectly  reflecting  sur&bces. 

A  comparison  oi  the  streaks  obtained  in  the  transmitted  and  in 
the  reflected  light  shows  that  never  do  two  of  such  streaks  cover 
one  another,  and  that  neither  do  the  former  lie  each  in  the  middle 
between  two  of  the  latter. 

As  to  change  of  position  of  the  streaks  with  the  angle  of  inci- 
dence, it  result^  that  in  the  light  polarized  parallel  to  the  plane  of 
incidence,  and  likewise  in  natural  bght,  the  position  was  as  good  as 
independent  of  the  angle  of  incidence ;  but  in  the  light  polarized 
perpendicular  to  that  plane  the  streaks  have,  up  to  a  certain  angle 
of  incidence,  which  amounted  to 


Air. 


Benzine, 
about  62^, 


Sulphide  of  carbon, 
about  52°, 


the  same  position  as  in  the  paraUel-polarized,  and  then,  with  a 
small  alteration  of  the  incidence-angle,  suddenly  suffer  a  disj^laoe- 
ment  characterized  by  the  appearance  of  the  streak  ihe  details  of 


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Intelligence  and  Miscellaneous  Articles.  233 

which  are  given  in  the  first  column  under  B.  Accordingly,  for 
angles  ^eater  than  those  given,  the  above  Tables  hold  good. 

Precisely  the  same  phenomena  as  on  the  ground  and  polished  salt 
may  be  observed  on  crystals.  Just  so  are  they  exhibited  on  per- 
manganate of  ammonia ;  but  here  measurements  were  impossible, 
on  account  of  the  great  decomposability  of  the  salt. 

The  above  observations  were  verified  in  every  way  possible.  For 
example,  the  dependence  of  the  situation  of  the  streaks  on  the  index 
of  refraction  was  again  established  by  putting  benzine  and  sulphide 
of  carbon  in  layers  one  above  another,  immersing  a  glass  plate 
coated  with  polished  permanganate  of  potassium,  and  comparing 
immediately  the  spectra  of  the  light  reflected  at  the  boundaries  of 
the  two  media  by  the  permanganate.  The  streaks  in  the  spectrum 
of  the  fight  which  had  passed  through  the  sulphide  of  carbon  were, 
in  relation  to  those  in  the  spectrum  of  that  which  had  traversed 
the  benzine,  displaced  towards  the  blue. — Poggendorff's  AnnaleUy 
1874,  No.  4,  pp.  625^628. 


ON  THE  TEMPERATURE  OP  THE  SUN.       BY  J.  VIOLLE. 

I  have  previously  indicated  and  discussed  the  method  I  most 
frequently  employ  in  my  measurements  concerning  the  temperature 
of  the  sun.  I  shall  today  describe  the  apparatus  I  use,  and  shall 
develop  the  calculus  of  the  experiments. 

My  apparatus  is  composed  of  two  concentric  spherical  envelopes 
of  brass.  The  interior  one,  15  centims.  in  diameter,  constitutes 
the  enclosure,  in  the  centre  of  which  is  the  bulb  of  the  thermometer 
submitted  to  experiment.  This  enclosure,  blackened  on  the  inside, 
is  kept  at  a  constant  temperature  by  a  continuous  current  of  water 
furnished  by  the  conduit-pipes  of  Uie  city  and  circulating  between 
the  two  balls.  The  exterior  ball  has  a  diameter  of  23  centims. ;  it 
has  been  carefully  polished  on  its  outer  surface,  and  is,  besides, 
protected  by  screens  which  leave  free  only  the  admission-aperture. 
This  aperture  is  at  one  of  the  extremities  of  a  brass  tube  17*5  mil- 
lims.  in  diameter,  directed  along  one  of  the  radii  of  the  sphere,  and 
opening  at  the  other  end  into  the  inner  ball.  The  free  extremity 
of  the  admission-tube  carries  a  movable  diaphragm  pierced  with 
three  circular  apertures  of  different  sizes.  Three  other  tubes  tra- 
verse, in  radial  directions,  the  space  comprised  between  the  two 
spheres :  two  of  them,  placed  one  at  45°,  the  other  at  90°  from  the 
admission-tube,  serve,  the  one  or  the  other  according  to  circum- 
stances, to  give  passage  to  the  stem  of  the  thermometer ;  the  third, 
closed  by  ground  and  slightly  blackened  plate  glass,  is  directed 
along  the  prolongation  of  the  admission-tube,  and  permits  the 
ascertaining  that  the  solar  rays  fall  exactly  on  the  bulb  of  the  ther- 
mometer. The  suitable  orientation  of  the  apparatus  is,  besides, 
attained  without  difficulty,  thanks  to  its  spherioil  form,  which  per- 
mits it  to  be  turned  gradually  in  the  wished-for  direction  upon  a 
circular  ring  which  serves  as  its  support. 


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234 


Intelligence  and  MisceUanema  Articles. 


The  following  is  the  course  of  an  experiment : — All  the  tubes 
being  carefuUy  closed,  and  the  thermometer  in  place,  the  tempera- 
ture (which  is  stationary  if  all  has  been  well  regulated  for  a  suffi* 
dent  time)  is  read ;  then  the  admission-tube  is  opened  after  bring- 
ing opposite  to  it  such  aperture*  of  the  diaphiagpn  as  is  judged 
suitable.  Now,  the  apparatus  being  kept  in  accurate  orientation, 
we  wait  until  the  temperature  again  becomes  stationary,  and  then 
note  the  excess  shown  by  the  thermometer. 

Experiment  shows  that  this  excess  depends  both  on  the  thermo- 
meter employed  and  on  the  diameter  of  the  aperture  of  admission. 
No  precise  ccmclusion,  therefore,  can  be  drawn  from  experiments  m 
which  we  have  not  preoccupied  ourselves  with  the  dimensions  of 
the  thermometer,  and  with  the  magnitude  of  the  admission-ap^ture 
pierced  in  the  enceinte,  with  the  temperature  constant.  On  the 
contrary,  by  employing  in  succession  different  thermometers  and 
different  apertures  of  the  diaphragm,  we  can  evaluate  very  accu- 
rately : — (1)  the  cooling  due  to  the  contact  of  the  air ;  (2)  the  heat- 
ing which  proceeds  from  the  radiation  of  the  portion  of  the  sky 
bordering  the  sun  and  seen  at  the  same  time  from  the  bulb  of  the 
thermometer.  I  shall  show  this  by  an  example,  the  data  of  which 
I  take  from  one  of  my  last  series  of  observations. 

On  the  20th  of  June  last,  operating  successively  with  two  ther- 
mometers, the  spherical  reservoirs  of  which  had  the  diameters  12 
millims.  and  7  miDims.  respectively,  and  with  three  different  aper- 
tures a,  6,  c  of  the  diaphragm,  the  respective  diameters  of  which 
were  17*5, 14*5,  and  12  milluns.,  I  obtained  the  following  results : — 


Time. 

the  enceinte. 

Temperature  of  the 

Temperature  ctf  the 
•mall  thermometer. 

h   m 
240 
255 
3  10 
3  30 

3  45 

4  10 
4  SO 
4  35 

1410 
14U6 
1405 
1400 
13*95 
13-90 
13-85 
13-30 

2?03  (diaphragm a) 
26-56  (diaphragm  h) 

24-05  (diaphragm  h) 
23-63  (diaphragm  c) 
23*85  (diaphragm  a) 

28-43  ((Saphraga  a) 
23-30  (diaphragm  «) 

28-05  (diaphragm  a) 

Let  us  take  first  the  observations  of  2*  55"  and  3^  10* ;  these 
two,  made  nearly  at  the  same  time,  should  lead  to  sensibly  equal 
excesses  of  temperature.  The  considerable  difference  between  the 
two  numbers  observed  arises  from  the  complication  introduced  into 
the  experiment  by  the  presence  of  air ;  to  the  radiation  from  the 
bulb  of  the  thermometer  is  added  the  cooling  produced  by  the  air ; 
and  in  these  two  ways  the  bulb  loses  a  quantity  of  heat  equal  to 
that  which  it  receives  from  the  sun.  The  loss  of  heat  in  vacuo, 
making  equilibrium  with  the  same  quantity  of  heat  received  from 
the  sun,  would  therefore  be  equal  to  the  loss  observed  plus  the  loss 
due  to  the  air.     But,  according  to  Bulong  and  Petit,  the  lowering 


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Intelligence  and  Miacellaneoue  Articles.  235 

of  temperature  resulting  from  this  last  cause  can  be  represented  by 

g  r>**^,  m  being  a  constant  dependent  only  on  the  elasticity  of  the 

air,  and  r  the  observed  excess.     We  should  have,  then,  in  vacuo 
with  the  two  thermometers  the  two  equal  excesses 

12-6H-^12-51»«»=10+^10>-233,  whence  w=2-24. 
o  3-5 

Let  us  take  in  the  same  way  the  observations  of  3^  45"^,  4^,  and 
4^  20™,  all  three  made  with  the  same  diaphragm,  but  different  from 
the  preceding  one;  they  conduct  to  the  equation 

9.77-1.  ;^9-77»««»=12-15+  ^12-15>«»,  whence  m=2-09. 
3*5  0 

Let  us  adopt  for  the  value  of  the  coefficient  of  cooling  m  the  mean 
of  the  two  values  thus  obtained,  ms=2'15 ;  with  the  aid  of  this  co- 
efficient we  can  draw  up  the  following  Table  of  the  temperatures 
which  would  have  been  observed  in  vacuo : — 


Time. 

Temperature  of 
the  enceinte. 

Temperature  of  the 
large  thermometer. 

Temperature  of  the 
imall  thermometer. 

h   m 
2  40 

2  55 

3  10 
330 

3  45 

4  0 
4  20 
4  35 

1410 
1405 
14*05 
14-00 
13-95 
1390 
13-85 
13*80 

3l-40(dUphragma) 
34-61  (diaphragm  h) 

34-54  (diaphragm  ») 
33*65  (diaphragm  c} 
34-20  (diaphragm  a) 

38  50  (diaphragm  a) 
33*10  (diaphragm  a) 

33^83  (diaphragm  a) 

On  tracing  the  curve  representing  the  course  of  the  thermometer 
for  one  and  the  same  admission-aperture,  it  is  readily  recognized 
that  the  relative  temperatures  at  the  different  periods  all  combine 
with  perfect  regularity,  whether  they  come  from  the  large  or  the 
small  thermometer. 

Let  us  now  consider  two  experiments  made  with  different  dia- 
phragms ;  and  as  the  small  thermometer  is  that  which  approximates 
most  nearly  to  the  theoretical  conditions  (especiaUy  for  small  ad- 
mission-apertures), let  us  take  the  three  experiments  relative  to 
3^  10",  3**  30",  and  3**  45".  Making  use  of  the  curve  of  the  tem- 
peratures for  the  diaphragm  a,  and  reducing  all  to  one  and  the 
same  temperature,  14°,  of  the  enceinte,  we  have  for  the  tempera- 
tures at  one  and  the  same  period: — 

Diaphragm  a  34*45 

Diaphragm  h   34-08 

Diaphragm  c  33*70 

Applying  to  these  data  the  equation  I  established  in  my  previous 


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236  IiUelligenee  and  Miscellaneoui  Articles. 

note, 

Sa«=Sa+*»a'+Oay  or  fl^— a'=  ^0*+ -^  of, 
we  have 

(Dii^h.  a)  l-0077»***-l-0077>*«  igieo  ^'^^^'^' 

+  (0.0009493- ^g3^)l.0077.. 

(Diaph.  6.)  l-0077»*w-l-0077"»  jg^  1-0077' 

whence  x=1355°,  and 
(Diaph.  a)  l-0077"«-l-0077'«=  1^60^'^^'^'^' 


(Diaph.  c)  l-0077«-'-10077'«=  Jg^o  ^'^'^'^' 


(0-0009493- ^^)10077», 
'*- 18^60 1-0077' 


whence  a? =1363°. 

The  agreement  of  the  two  values  of  x  shows  that  the  correction 
necessitated  by  the  radiation  of  the  region  of  the  sky  in  the  vicinity 
of  the  sun  is  made  with  sufficient  exactness  by  writing  for  the  total 

radiation  of  the  different  portions  of  this  surface  ^  of,  as  if  all 

these  parts  were  at  one  and  the  same  mean  temperature  y. 

Therefore,  in  the  example  selected,  it  will  be  concluded  from  these 
calculations  that,  on  the  20th  June,  at  Grenoble,  the  temperature 
of  the  sun,  defined  as  I  have  indicated  above,  was,  at  3^  30'°, 

1354°. 

But  this  number  itself,  to  give  the  true  temperature  of  the  sun, 
ought  to  be  further  corrected  on  account  of  divers  influences,  par- 
ticularly the  absorption  of  the  terrestrial  atmosphere.  It  is  chiefly 
by  operating  at  different  altitudes,  and  (of  course)  noting  the  pres- 
sure and  the  hygrometric  state  of  the  air  at  each  station,  that  I 
hope  to  solve  this  problem.  For  this  purpose  I  have  already  made 
several  ascents  of  the  Alps ;  and  I  shall  resume  them  as  soon  as 
possible. — Comptes  Bendus  de  TAcad.  dt$  Sciences,  June  29,  1874. 


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Intelligence  and  Miscellaneous  Articles,  237 


PHYSICS  OF  THB  INTERNAL  EARTH. 
BY  D.  VAUGHAN. 

In  1853  I  first  attempted  to  trace  the  consequences  of  subter- 
ranean heat,  bj  taking  into  consideration  some  facts  and  principles 
which  seemed  to  l^ave  received  but  little  attention.  The  results  of 
my  inquiries  on  the  subject  were  given  in  a  circular  in  1854,  in  a 
pamphlet  in  1856,  and  in  a  paper  which  I  sent  to  the  British 
Association  in  1861,  and  of  which  an  abstract  is  published  in  the 
Eeports  of  the  Sections,  page  134.  In  that  paper  I  endeavoured 
to  show  that  the  terrestrial  crust,  if  reposing  on  lava  of  a  declining 
temperature,  would  receive  accessions  of  buoyant  solid  material, 
chiefly  on  such  points  as  extend  deep  into  the  fiery  menstruum,  and 
that  the  consequent  growth  of  internal  mountains  would  be  inter- 
rupted only  by  the  occasional  movements  of  vast  portions  of  this 
light  matter  to  positions  much  higher  than  those  at  which  they  were 
first  deposited.  To  the  collisions  of  such  rising  masses  against  the 
weaker  parts  of  the  earth's  crust  I  ascribe  eiurthquakes ;  but  the 
theory  affords  a  more  satisfactory  explanation  for  volcanic  phe- 
nomena. 

Avalanches  of  siliceous  rocks,  ascending  through  buoyimcy  from 
deep  subterranean  peaks  or  depressions,  would  lead  to  important 
results  by  conveying  heat  from  a  lower  to  a  higher  stratum  of  the 
internal  earth.     Owing  their  solidity  to  pressure,  such  stony  masses 
would  fuse  during  the  ascent ;  and,  like  our  mountain-floods,  would 
erode  channels  which  must  for  a  long  period  direct  them  to  the  same 
localities.     The  same  spots  of  the  earth's  crust,  being  thus  exposed 
for  many  ages  to  the  repeated  inroads  of  intensely  heated  matter 
from  great  depths,  would  be  reduced  in  thickness  by  the  frequent 
fusion,  and  would  present  a  weaker  barrier  to  subterranean  vio- 
lence.   Such  an  internal  convection  of  heat  would  end  in  perforating 
the  earth's  crust  and  producing  an  immense  lake  of  lava  on  its  sur- 
face, were  it  not  for  the  cooling  influence  of  aqueous  action ;  and  the 
presence  of  water  on  our  globe,  though  tending  much  to  increase 
the  violence  of  earthquakes  and  volcanic  eruptions,  has  the  effect  of 
confining  their  ravages   within  a  more  limited  range.     To  the 
absence  of  water  from  the  moon  we  may  ascribe  the  enormous 
diameters  of  the  craters  of  lunar  volcanoes ;  while  their  height  is 
displayed  on  a  far  less  scale,  and  there  are  no  long  ranges  of  lunar 
mountains.     On  our  satellite  also  volcanoes  have  for  the  most  part 
an  insular  character,  conforming  little  to  the  linear  arrangement  so 
common  on  the  earth ;  so  that  the  cooling  agency  of  water  appears 
to  have  been  concerned  in  producing  the  vast  rents  or  fissures  on 
which  so  many  volcanic  ormces  seem  to  be  located. 

Apart  from  the  evidence  which  the  pendulum  and  geodetic  mea- 
surements give  of  inequalities  on  the  invisible  side  of  the  earth's 
crust,  it  can  be  proved  theoretically  that  they  are  inevitable  in  the 
course  of  solidification  over  the  molten  mass.  One  source  of  solid 
matter  light  enough  to  form  the  external  framework  of  our  globe 


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238  Intelligence  emd  Miscellaneous  Articles. 

is  to  be  found  in  the  decomposition  of  many  of  the  heavy  silicates 
by  enormous  pressure  when  the  temperature  of  the  menstruum  in 
which  they  were  fused  sunk  below  the  melting-point  of  quartz. 
An  equivalent  of  oxide  of  lead  and  of  crystallized  silicic  acid  would 
have  their  common  volume  increased  about  14  per  cent,  on  comlH' 
ning  and  forming  lead  glass.  Now,  at  a  depth  of  1000  kilometres 
below  the  earth's  surface,  the  pressure  is  equal  to  about  300,000 
atmospheres ;  and  accordingly  the  formation  of  a  cubic  inch  of 
glass  by  the  union  of  quartz  and  oxide  of  lead  would,  in  conse- 
quence of  the  expansion  it  involves,  be  resisted  by  a  force  the  ther- 
mal equivalent  of  which  may  be  represented  by  the  heat  expended 
in  melting  14  cubic  inches  of  ice.  A  force  of  equal  energy  would 
be  exerted  by  the  same  pressure  for  the  decomposition  of  a  cubic 
inch  of  silicate  of  lead,  in  the  supposed  locality,  and  for  the  crys- 
tallization of  tiie  resulting  silicic  acid.  As  far  less  heat  is  evolved  by 
the  union  of  the  strongest  adds  and  bases,  and  as  a  crystallization 
or  atom-arrangement  can  make  no  heavy  demands  on  force,  it  is 
reasonable  to  conclude  that  in  the  supposed  case  chemical  affinity 
would  be  overruled  and  that  the  silicate  ai  lead  would  be  decom- 
posed. From  similar  estimates  it  would  also  appear  that  other 
silicates,  especially  those  of  heavy  metals,  would  undergo  a  similar 
decomposition  at  great  depths,  and  would  part  with  their  silica 
when  the  temperature  became  low  enough  to  allow  its  solidification. 

Another  source  of  buoyant  matter  is  to  be  found  in  the  transfer 
of  silica  from  the  heavy  metallic  oxides  to  the  alkalies  and  other 
strong  bases.  The  light  compounds  thus  formed  would,  according 
to  Delesse  and  Deville,  contract  more  than  other  igneous  rocks  in 
passing  into  a  solid  state  ;  and  it  is  evident  that  in  propcnrtion  to 
this  contraction  vnll  their  production  be  favoured  by  pressure  on  the 
decline  of  the  primitive  heat.  The  growth  of  a  floatmg  crust  would 
also  be  promoted  by  other  circumstances.  Of  many  of  the  metallic 
oxides,  the  most  infusible  compounds  are  those  in  which  the  silicic 
acid  is  very  small  or  in  a  very  large  proportion.  But  the  latter 
bodies,  which  have  almost  invariably  the  lowest  specific  gravity, 
bave  also  their  fusibility  reduced  most  by  pressure  m  consequence 
of  the  contraction  which  they  undergo  in  assuming  a  solid  form. 
On  this  point  more  satisfactory  evidence  may  be  obtained  by  an 
investigation  similar  to  that  of  Clausius,  but  in  which  the  effects  of 
pressure  upon  fusion  is  determined  frcmi  the  change  of  volume  and 
the  modulus  of  elasticity. 

Of  tJie  various  products  which  separate  from  the  subterranean 
lava  in  cooling,  the  most  dense  parts  would  sink  to  the  centre, 
though  solidifying  in  the  uppermost  stratum ;  while  the  li£;hter 
material,  though  taking  the  solid  form  at  great  depths,  would  rise 
towards  the  surface.  But  the  solidity  of  the  light  silicated  matter 
could  be  permanmit  only  when  kept  under  the  influence  of  immense 
pressure,  by  settling  on  prominent  points  which  extend  from  the 
inner  side  of  the  crust  deep  into  the  lava.  The  great  centres  of  ac- 
cumulation of  this  buoyant  matter  must  be  under  continents,  where 


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Intelligence  and  Miscellaneous  Articles.  239 

the  eArtb's  crust  has  evidentlj  the  greatest  thickziess  and  reposes 
on  the  deepest  internal  prominences ;  and  to  the  ocoasional  slides 
and  asc^iding  movements  of  matter  from  these  parts  ot  the  subter- 
ranean regicMis,  we  may  ascribe  the  prevalence  oi  vulcanicity  on  so 
many  continental  coasts. 

If  only  one  per  cent,  of  terrestrial  matter  passed  into  a  solid  form 
in  the  course  of  ten  miUicms  of  years,  there  would  be  still  sufficient 
grounds  for  assigning  to  rock-slides  a  mass  so  great  that  the  me* 
chanical  effects  of  their  collisioos  against  the  thinner  parts  of  the 
crust  mayproduce  the  most  violent  earthquake  shocks.  But  the  most 
obvious  efcecta  must  be  ascribed  to  the  sudden  elevation  of  tempera- 
ture which  the  thin  spots  of  the  earth's  crust  should  experience, 
and  which  may  be  reasonably  estimated  at  many  thousand  degrees. 
Exposed  to  such  a  fierce  heat,  the  solid  structure  would  be  rent  by 
the  unequal  expansion  of  its  parts,  or  by  the  elasticity  of  its  volatile 
constituents.  8team  would  manifest  an  irresistible  power  when 
rock  containing  moisture  tumbled  into  tlie  molten  liquid  or  encoun- 
tered it  wh^i  penetrating  through  fissures.  But  a  motive  power 
of  long  continuance  would  arise  from  the  property  which  silica  has 
pf  expelling  other  acids  from  bases  at  high  temperature.  As  the  si- 
liceous rocks  come  into  coUisicm  with  the  strata  containing  limestone 
or  any  other  carbonates,  the  resulting  mass  should  swell  with  the 
evolution  of  carbonic  acid,  and  boil  over  a  volcanic  crater  or  even 
open  a  new  (me.  In  consequence  of  the  pressure,  this  expulsion  of 
carbonic  acid  will  require  a  higher  temperature ;  and  the  cooling, 
chiefly  through  the  agency  of  water,  would  soon  occasion  a  state  of 
repose  until  there  occurred  a  new  influx  of  heated  matter  from 
deep  regions.  An  estimate  of  the  rate  of  cooling,  as  invdved  in 
the  mere  production  of  steam  alone,  would  show  that,  during  their 
numerous  eruptions,  Etna  and  Vesuvius  must  have  1/ost  a  quantity 
of  heat  too  great  to  be  supplied  by  any  conceivable  chemical  or 
mechanical  action  in  their  immediate  vicinity ;  and  evidence  may  be 
thus  obtained  of  the  necessity  of  the  convection  of  caloric,  and  of 
the  introduction  of  incandescent  matter  from  distant  localities  to 
the  theatre  of  volcanic  activity. 

CiDcinoati^  0.,  July  16, 1874. 


ON  THE  CONVERSION  OF  ORDINARY  INTO  AMORPHOUS  PHOS- 
PHORUS BY  THE  ACTION  OF  ELECTRICITY. 

In  the  Anzeiger  of  the  Imperial  Academy  at  Vienna,  Professor 
V.  Schrotter  gives  the  following  notice  of  this  transformation,  dis- 
covered by  Dr.  Geissler : — 

Already  in  1860  Dr.  Qeissler  endeavoured  to  show  that  electri- 
city by  itself  effects  this  change ;  and  he  had  the  goodness,  on  the 
occasion  of  his  visit  to  Vienna  at  the  time  of  the  Universal  Expo- 
sition, to  give  up  to  me  some  of  the  glass  apparatus. 

The  simplest  of  these  is  an  exhausted  glass  tube  of  about  35  cen- 


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240  Intelligence  and  Miscellaneotu  Articles* 

tims.  length  and  2  centims.  diameter,  to  the  ends  of  which  additions 
were  attached  (by  fusion)  containing  the  conducting-wires,  so  that 
in  the  experiment  the  wires  were  at  least  45  centims.  distant  from 
each  other.  The  tube  was  filled  with  phosphorus  vapour  of  very 
little  tension ;  after  the  experiment  its  sides  were  coated  with  a 
thin  layer  of  amorphous  phosphorus  brownish  red  changing  to 
ffolden  yellow,  and  in  many  places  exhibiting  the  colours  of  thin 
films. 

The  second  apparatus  serving  for  the  same  purpose,  a  master- 
piece of  the  glassblower's  art,  has  the  form  and  sue  of  a  beaker- 
shaped  double-walled  champagne-glass.  The  thin  layer  of  amor- 
phous phosphorus  distributed  over  the  inner  surfaces  of  its  walls 
exhibits  the  play  of  all  the  colours  of  thin  films,  giving  to  the  glass 
a  pleasing  appearance. 

The  third,  still  more  elaborately  executed  apparatus  is  designed 
to  show  that  the  conversion  of  the  phosphorus  is  effected  even  by 
the  inducing  action  of  the  current.  For  this  purpose  the  ends  of 
the  two  aluminium  conductin^-wires  are  inserted  in  exhausted 
spheres  in  which  there  is  no  phosphorus.  These  spheres  are  en- 
closed in  others,  which  are  united  by  a  tube  40  millims.  long  and  1 
millim.  wide.  The  interspaces  thus  formed,  likewise  exhausted, 
contain  the  phosphorus,  which  is  therefore  completely  shut  off  from 
the  conducting-wires  by  a  wall  of  glass.  The  distance  between  the 
conducting-wires  amounts  to  26,  and  the  diameter  of  the  outer 
spheres  to  5  centims.  The  interval  between  the  walls  of  the 
spheres  amounts  to  5  millims.  Here  also  the  inner  side  of  the 
outer,  and  the  outer  side  of  the  inner  sphere,  in  like  manner  as 
above  stated,  were  coated  with  amorphous  phosphorus.  Only  in 
the  narrow  connexions  was  no  phosphorus  deposited. 

The  above-mentioned  facts  furnish,  perhaps,  the  best  demonstra- 
tion that  the  conversion  of  phosphorus  into  the  amorphous  modifi- 
cation is  effected  neither  by  the  light  nor  by  the  heat  which  accom- 
pany the  current,  but  exclusively  by  the  electricity  itself. 

The  instructive  experiments  which  Hittorf  published  in  1865 
(Pogg.  Ann.  vol.  cxxvi.  p.  195)  were  made  with  another  arrange- 
ment of  the  apparatus,  as  the  platinum  wires,  fused  into  glass 
spheres  of  6  to  8  centims.  diameter,  were  only  a  few  millims.  dis- 
tant from  one  another ;  so  that  sparks  passed,  and  the  course  of 
the  phenomenon  was  somewhat  different  from  that  above  described ; 
but  the  conclusions  deduced  therefrom  by  Bittorf  were  the  same. 

I  hope  to  be  able  to  resume  this  subject  in  greater  detail ;  for 
the  present  the  above  account  may  suffice  to  recall  attention  to  it. 
— Poggendorff's  Annalen^  vol.  clii.  pp.  171-173. 


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THE 
LONDON,  EDINBURGH,  and  DUBLIN 

PHILOSOPHICAL    MAGAZINE 

AND 

JOURNAL   OF   SCIENCE- 


[FOURTH  SERIES,] 


OCTOBER  1874. 


XXXIV •  On  Gladstone's  Experiments  relating  to  Chemical  Mass. 
By  Edmund  J.  Mills,  D.Sc,  F.R.S* 

I.  rpHE  Philosopbical  Transactions  for  1855  (vol.  cxlv.)  con- 
J-  tains  an  important  memoir  by  Gladstone  "  On  Cirenm- 
stances  modifying  the  Action  of  Chemical  Affinity/'  In  this 
memoir  numerous  sets  of  experiments  are  described,  which 
mainly  serve  to  determine,  by  means  of  an  increase  or  diminu- 
tion of  colour,  the  progress  of  certain  selected  reactions.  The 
results  are  exhibited  in  curves,  several  of  which  show  a  regular 
course,  while  all  are  continuous ;  but  no  mathematical  expres- 
sion of  the  law  of  action^  is  given.  About  eleven  years  after- 
wards (Phil.  Trans.  1865-6)  it  was  shown  by  Esson,  on  the 
basis  of  Harcourt's  experiments,  that  when  a  substance  under- 
goes chemical  change,  the  residue  y  of  changing  substance  is 
connected  with  the  unit  intervals  x  of  change  (time,  reagent,  or 
other  operator)  by  the  equation 

where  a  represents  the  amount  of  substance  originally  present, 
and  « the  amount  of  it  disappearing  ])er  unit  o(x.  This  relation 
is  graphically  represented  as  a  logarithmic  curve ;  but,  as  a  rule, 
even  in  very  simple  cases,  its  expression  is  more  complex,  and 
corresponds  to  the  form 

which  indicates  that  two  bodies  are  undergoing  change,  or  that 
one  body  is  undergoing  dual  change.     In  cither  case  the  amount 

♦  Communicated  by  the  Author. 
Phil.  Mag.  S.  4.  Vol.  48.  No.  318.  Oct.  1874.  R 


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242  Dr.  E.  J.  Mills  on  Gladstone's  Experiments 

of  change  per  unit  interval  is  proportional  to  the  amount  of  sub- 
stance then  changing. 

As  Gladstone's  results  were  the  first  in  which  the  continuity 
of  the  chemical  process  was  experimentally  demonstrated  (at  any 
rate  on  a  sufficient  scale)^  I  felt  much  interested  in  ascertaining 
whether  Esson's  equation  would  apply  to  them^-especially  when 
I  considered  how  few  have  been  the  contributions  to  chemical 
dynamics^  the  laborious  (and  consequently  unpopular)  nature  of 
such  researcheSi  and  the  inexpediency  of  allowing  good  work  to 
remain  dumb  or  unexpressed. 

II.  The  colorimetrical  method^  which  was  used  throughout  by 
Gladstone,  has  considerable  disadvantages,  and  is  most  service- 
able when  only  small  quantities,  as  in  the  case  of  the  Nessler 
test,  have  to  be  measured  and  an  inaccuracy  of  about  5  per  cent, 
is  of  no  consequence.  It  is  probable  that  the  observer's  estimate 
of  colour  varies  during  a  long  course  of  experiments,  and  is 
really  under  training  in  the  earlier  ones;  so  that,  as  will 
actually  be  found  below,  all  the  more  serious  errors  occur,  as  a 
rule,  at  the  outset.  We  must  also  remember  that  colour-effects 
in  solutions  are  not  unfrequently  slow  in  attaining  their  maxi- 
mum, thus  making  a  particular  observation  too  low;  on  the 
other  hand,  the  subsequent  arrival  of  this  maximum  will  make 
a  following  observation  too  high :  hence  also,  by  virtue  of  com- 
pensation, the  later  observations  may  be  expected  to  be  mora 
correct. 

A  further  difficulty  lies  in  the  computation  itself.  The  amount 
of  chemical  energy  (or  substance)  originally  present  is  not  given 
in  terms  of  the  reagent,  and  has  to  be  arrived  at  by  successive 
and  wearisome  approximations;  and  these  might  perhaps  have 
been  carried  a  stage  further  with  advantage.  Again,  the  sue- 
cessive  values  of  a  are  very  seldom  given  in  the  experiments, 
which  had  not  been  arranged  to  test  any  particular  hypothesis; 
they  had  consequently  to  be  obtained  by  graphic  interpolation 
on  curves  which,  for  such  a  purpose,  should  have  been  consider* 
ably  longer. 

If  we  bear  in  mind  these  and  other  drawbacks,  we  shall  regard 
the  coincidence  between  theory  and  experiment  as  very  striking. 

III.  Ferric  Nitrate  and  Potassic  Sulphoct/anide  [loc.  cii.  p.  187, 
pi.  7.  fig.  1). — ^To  one  *' equivalent ''  of  ferric  nitrate  successive 
groups  of  '^  equivalents ''  of  potassic  sulphocyanide  are  added, 
in  presence  of  water;  the  amount  of  "red  salt  produced*^  is 
estimated  by  eye-observations,  the  liquid  being  diluted  for  that 
purpose  up  to  a  standard.  The  total  amount  a  of  red  salt  thus 
producible  represents  in  special  measure  the  original  unexhausted 
energy  of  the  nitrate.  I  have  taken  each  unit  of  x  as  represent- 
ing 25  ''  equivalents  "  of  potassic  sulphocyanide.     The  equation 


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relating  to  C/iemical  Mass. 


243 


19 


y=401(-8550)'+224(-1516)'; 

bat  the  results  are  expressed  in  percentages  of  the  initial  value 
ofy. 

Tablb  I. 


a. 

y,  calculated. 

jff  found. 

1 

60-3 

60-2 

2 

477 

477 

3 

40-2 

39-2 

4 

34*3 

330 

5 

29-3 

28-5 

6 

251 

24-5 

7 

21-4 

20-6 

8 

183 

178 

9 

15-7 

15-4 

10 

13-4 

13-3 

11 

11-5 

117 

13 

9-8 

10-4 

13 

8-4 

8-8 

14 

71 

7-2 

15 

61 

61 

Gladstone  gives  two  variations  of  this  experiment. 

IV.  Ferric  Sulphate  and  Potassic  Sulphocyanide  {loc.  cU. 
p.  189,  pi.  7.  fig.  1). — On  accouut  of  the  weakness  of  the  colour 
produced  when  a  sulphate  is  present,  the  amount  of  the  salts 
employed  was  doubled.  One  equivalent  of  ferric  nitrate  was 
taken.     The  equation  is 

y=488  {-8208)'+ 182  (-1400)'; 

and  the  unit  of  x  is  15  equivalents. 

Table  II. 


X. 

y,  calculated. 

y,  found. 

1 

66-3 

653 

2 

b2'2 

53-9 

3 

42-6 

44-2 

4 

34*9 

35-6 

5 

28-6 

287 

6 

23-5 

237 

7 

19-3 

19-6 

8 

15-8 

15*3 

9 

13-0 

12-0 

10 

10-7 

96 

11 

87 

81 

12 

7-2 

6-7 

13 

5-9 

5-6 

R2 


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244  Dr.  E.  J.  Mills  an  Gladstone's  Experimenti 

V.  Ferric  Chloride  and  Potctmc  Sulphocyanide  (loc.  ^ii.  p.  189, 
pi.  7.  fig.  1). — ^This  experiment  is  described  as  "precisely  ana- 
logous to  the  preceding.^'    The  equation  is 

y=406  (•8900)'+214  (-2500)'; 

and  the  unit  of  x  is  20  equiyalents. 

Table  IIL 


4r. 

y,  calcnltted. 

y,  found. 

66-9 

65*0 

54H) 

34-0 

467 

46-9 

41  •« 

41-9 

36-6 

36-8 

39*6 

83-9 

99-0 

99-5 

95-8 

95*8 

99-9 

99-9 

10 

90-4 

900 

11 

18-9 

173 

19 

169 

14-8 

VI.  Ferric  Nitrate  and  Hydric  Sulphocyanide  {loc.  cit.  p.  190, 
pi.  8.  fig.  2). — ^Ferric  nitrate,  1  equivalent.  Unit  of  ^  =  4  equi* 
Talents.     The  equation  is 

y=533B  (-91093)' +89-5  (-82670)'. 
Table  IV. 


4*. 

y,  ctlculaied. 

y»  found. 

1 

89-7 

897 

9 

72-6 

731 

3 

653 

65-3 

4 

59  1 

58*9 

5 

538 

53-9 

G 

49^ 

496 

7 

446 

45-3 

8 

406 

413 

9 

370 

37^ 

10 

•    337 

34-4 

11 

30  7 

319 

The  above  results  seem  to  have  been  the  sequel  of  consider- 
able experience  with  the  method,  and  are  in  exceptional  ac- 
cordance with  theory. 

VII.  Ferric  Citrate  and  Hydric  Gallate  {loc.  cit.  p.  193,  pi.  9. 
fig.  1). — One  equivalent  of  ferric  citrate  was  mixed  with  6  kc 
equivalents  of  hydric  gallate,  and  the  increasing  black  coloration 
measured.     Unit  of  or  =  3  equivalents.    The  equation  is 

y=660  (•9127)'+90  (•8072)'. 


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relating  to  Chemical  Mass. 
Table  V. 


245 


4r. 

y,  calcnlated. 

y,  found. 

1 

840 

867 

2 

74-4 

•76  0 

3 

G72 

68-4 

4 

612 

621 

5 

65-8 

56-3 

6 

50-9 

50-8 

7 

464 

460. 

8 

42-4 

41-7 

9 

38-7 

380 

10 

85-3 

347 

11 

322 

321 

VIII.  Ferric  Citrate  and  Potassic  Ferrocyanide  {loc.  cit.  p.  199, 
pi.  9,  fig.  5). — One  equivalent  of  ferric  citrate  was  mixed  with  3 
&c.  equivalents  of  potassic  ferrocyanide  in  presence  of  bydric 
oxalate,  and  the  increasing  blue  coloration  determined.  Unit 
of  ;r  s  3  equivalents.     The  equation  is 

y=102  (•2010)'+23  (-7699)'. 
Table  VI. 


X, 

y,  calculated. 

y,  found. 

30-6 

29-6 

142 

11-4 

91 

9-8 

66 

6-4 

50 

4-0 

IX.  The  above  equations  represent  the  greater  part  of  Glad- 
stone's results  as  figured  at  the  end  of  his  memoir.  I  have  not 
worked  out  the  remainder,  either  (1)  because  they  form  mere 
continuations  or  repetitions  of  the  reduced  curves,  or  (2)  because 
the  experiments  were  not  numerous  enough,  nor  the  theory  of 
the  reactions  sufficiently  evident,  to  enable  the  calculation  to  be 
made.  The  curves  representing  the  formation  of  ferric  meco- 
nate  and  acetate  somewhat  resemble,  but  are  not  identical  with, 
the  cubical  parabola.  Similar  ones  are  drawn  by  Harcourt  and 
Esson  (Phil.  Trans.  1866,  pi.  17),  and  Guldberg  and  Waage 
{Etudes  sur  les  Affinit(s  chimiques,  Christiania,  1867,  pis.  14, 15, 
16).  It  is  obvious  that  they  represent  duplex  reactions ;  but 
their  complete  reduction  may  perhaps  be  a  matter  of  consider- 
able difficulty. 

In  order  to  estimate  the  accuracy  of  the  experimental  work, 
and  the  soundness  of  the  hypothesis  involved  in  its  symbolic 
^xpressioi)^  I  have  drawn  up  the  following  en*or  Table,  showing 


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246     On  Gladstone's  Experiments  relating  to  Chemical  Mass. 

a  sammary  of  the  differences  between  calcolation  and  observation^ 
as  compared  in  percentages. 

Table  VII. 


AboTe  S-3. 

Above  1-S 
(inclusive). 

Above  0-5-1-0 
(inclusive). 

Above  0HM)-5 
(inclusive). 

Table  I 

Table  II.    ... 
Table  III.  ... 
Table  IV.  ... 
Table  V.    ... 
Table  VI.  ... 

0 
0 
0 
0 

I 
0 

I 
3 
2 
0 
9 
0 

0 
6 
8 
6 
4 
8 

Total!    

1 

8 

2S 

86 

The  entire  number  of  comparisons  is  sixty-seven.  Thus  it 
appears  that  64  per  cent,  of  the  errors  are  such  as  would^  on 
their  average^  be  found  in  very  good  analytical  work ;  33  per 
cent,  of  them  occur,  on  their  average,  in  ordinarily  good  analy- 
tical work ;  the  remaining  13  per  cent,  lie,  on  their  average, 
within  the  usual  limits  allowable  in  colorimetry, 

X.  The  foregoing  equations  show  that  any  such  expression  as 

i[Fe«Cl«]  +  3KpNS=i[Fe*(CNS)«]  +  3KCI 

h  wholly  erroneous^  if  intended  to  represent  the  chemical  energy 
of  a  ferric  salt,  or  the  amount  of  potassic  sulphocyanide  that  is 
capable  of  acting  thereon;  for  the  energy  of  the  quantity 
i[Fe«Cl^  is  not  exhausted  until  about  400  units  (KCNS)  have 
been  brought  to  bear  upon  it ;  and  other  ferric  salts  are  repre- 
sented by  similarly  high  numbers.  The  ordinary  equations  of 
chemistry  represent  the  result  of  distributing  weight,  and  give 
no  account  of  work  done ;  these,  on  the  other  hand,  represent  » 
dynamical  process  as  well  as  distribution  of  weight.  Hence  it  is 
clear  that  the  '^equivalents^'  or  valencies  inferred  from  the  com- 
mon equations  rest  upon  a  wholly  fallacious  basis,  and  cannot 
be  depended  upon  in  scientific  reasoning.  To  assert,  for  instance, 
that  G  is  equivalent  to  U^,  amounts  to  stating  that  hydrogen 
and  carbon  have  been  compared  as  to  the  work  they  can  do 
under  certain  circumstances,  just  as  ferric  chloride  is  compared 
with  ferric  sulphate  in  Gladstone's  experiments.  No  such  re- 
search has,  however,  been  made ;  and  it  would  not  be  likely  to 

Q 

yield  the  ratio  TTi  =1  i^  it  were  made.    What,  then,  becomes  of 

the  doctrine  that  carbon  is  tetravalent  ? 

It  is  worthy  of  remark  that,  while  the  ordinary  equations  in- 
variably express  that  quantity  consists  of  parts  (that,  for  example^ 
potassic  chloride  contains  potassium  and  chlorine,  whereas  we 


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On  a  very  singular  Sulphuretted  Nitroffenoue  Confound.     247 

only  know  that  it  contains  the  joint  weights  of  potassium  and 
chlorine)^  the  logarithmic  equations  make  no  suggestion  upon 
this  subject.  All  the  above  experiments  might  have  been  accu- 
rately performed  and  symbolically  expressed  by  a  person  totally 
ignorant  of  the  ''constitution'*  of  ferric  salts  or  of  potassic  sul- 
ptioeyanide ;  and  the  reagent  might  have  been  extremely  impure, 
provided  that  it  produced  a  red  coloration.  What  we  owe  to 
Esson  and  Gladstone  we  might  have  inherited  from  Wenzel  or 
Cavendish, 

12  Pemberton  Terrace, 
8t.  John's  Park.  N. 


XXXV.  On  a  very  singular  Sulphuretted  Nitrogenous  Compound, 
obtained  by  the  Action  of  Sulphide  of  Ammonium  on  the  Hydrate 
of  Chloral.  By  Edmcnd  W.  Davy,  A.M.,  M.D.,  M.R.I, A., 
Professor  of  Forensic  Medicine,  Royal  College  of  Surgeons, 
Ireland,  and  late  Professor  of  Agricultural  Chemistry,  Royal 
Dublin  Society^. 

THE  substance  termed  hydrate  of  chloral,  or  chloral  hydrate, 
from  the  many  valuable  therapeutic  properties  it  has  re* 
oently  been  found  to  possess,  has  within  the  last  four  or  five 
years  been  prepared  in  considerable  quantities,  and  has  become 
an  article  of  some  commercial  importance;  and  numerous  as 
are  the  useful  applications  which  have  already  been  made  of 
that  substance  in  medicine,  there  can  be  but  little  doubt  that 
their  number  may  be  greatly  increased;  so  that  we  may  justly 
regard  chloral  hydrate  as  one  of  the  most,  if  not  the  most,  im- 
portant of  the  recent  additions  to  our  materia  medica. 

It  being  thus  a  substance  of  such  practical  importance,  any 
information  which  may  tend  to  extend  our  knowledge  of  its  che- 
mical properties  and  relations  should  not,  I  conceive,  be  regarded 
as  devoid  of  interest.  I  shall  therefore  briefly  state  the  results 
of  some  observations  which  I  have  recently  made  as  to  the  action 
of  sulphide  of  ammonium  on  that  substance  (a  subject  that  has 
been  but  little  studied),  and  describe  the  properties  of  a  very 
singular  compound  thereby  produced,  the  constitution  of  which, 
as  far  as  I  am  aware,  has  not  hitherto  been  determined. 

When  sulphide  of  ammonium  is  added  to  an  aqueous  solution 
of  chbral  hydrate,  the  mixture  after  a  few  moments  acquires  a 
deep  yellow  colour,  and,  rapidly  becoming  orange,  passes  to 
a  reddish  brown,  which  finally  assumes  so  dark  an  appearance 
that  the  liquid,  when  in  any  quantitv,  looks  almost  black  by 
reflected  light.      It  was  also  observed,  after  the  mixture  had 

*  Communicated  by  the  Author. 

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248  [Dr.  E.  W,  Davy  on  a  very  singular 

assumed  an  orange  tint,  that  almost  immediately  more  or  less 
of  a  solid  matter  invariably  separated  from  the  liquid^  appear- 
ing at  first  of  a  bright  orange  or  light  red  colour,  from  its  being 
suspended  in  the  orange  or  red  liquid,  but  that,  after  it  was 
separated  from  it  by  filtration  and  washing,  it  was  found  to 
possess  a  light  brown  appearance.  Whilst  the  changes  just  de- 
scribed were  taking  place,  it  was  also  noticed  that  the  mixture 
became  sensibly  warm  to  the  hand,  and  that  the  odour  of  the 
sulphide  disappeared,  whilst  that  of  ammonia  and  of  chloroform 
was  easily  detected. 

It  was  further  ascertained  that  when  the  dark  reddish-brown 
liquid  obtained  in  the  way  just  stated  was  acidified  with  an  acid, 
it  yielded  a  copious  brown  precipitate,  which,  though  somewhat 
darker  in  its  colour  than  that  which  separates  from  the  liquid 
before  the  addition  of  the  acid,  appears  to  be  essentially  the 
same  compound,  the  difference  of  shade  being  probably  due,  at 
least  in  some  measure,  to  different  amounts  of  free  sulphur 
present  in  each. 

As  the  principal  feature  of  interest  connected  with  the  reac- 
tion referred  to,  I  considered,  was  attached  to  the  formation 
of  the  brown  solid  compound  just  noticed,  a  quantity  of  it 
was  made  as  follows : — Four  hundred  grains  of  chloral  hydrate 
being  dissolved  in  about  ten  ounces  of  distilled  water,  sulphu- 
retted hydrogen  was  passed  through  the  solution  till  it  poss^sed, 
after  being  shaken,  the  odour  of  that  gas.  Sulphide  of  ammo- 
nium was  then  added  in  small  portions  at  a  time,  continuing 
the  passage  of  the  sulphuretted  hydrogen  through  the  mixture 
when  the  effects  before  described  were  produced.  This  treat- 
ment was  continued  till  no  further  action  appeared  to  take  place, 
and  the  mixture  possessed,  after  being  well  shaken,  a  strong 
odour  of  sulphuretted  hydrogen. 

I  ma^  here  observe  that,  after  the  addition  of  the  sulphide  of 
ammonium,  the  evolution  of  ammonia  was  from  the  first  percep- 
tible, whilst  the  odour  of  the  sulphide  and  of  the  gas  for  some 
time  continually  disappeared,  and  it  was  not  till  the  later  stages 
of  the  process  that  the  smell  of  chloroform  could  be  detected. 

To  the  mixture  so  treated,  which  was  distinctly  alkaline,  pure 
diluted  sulphuric  acid  was  added  till  it  acquired  an  acid  reaction, 
and  the  whole  was  thrown  on  a  filter,  when  the  brown  solid  was 
separated  from  a  deep  amber-coloUr^d  liquid.  The  former  was 
then  washed  with  cold  distilled  water  till  no  indication  of  sul- 
phuric acid  in  the  filtrate  could  be  detected  by  chloride  of  barium; 
but  finding  that  it  exhibited  traces  of  ammonia  when  treated  with 
caustic  lime,  the  washing  of  the  brown  solid  was  continued,  first 
using  cold  distilled  water ;  and  this  failing  to  accomplish  the 
object  sought,  it  was  washed  with  a  considerable  quantity  of  hot 


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Sulphuretted  Nitrogenous  Compound.  249 

distilled  water  till  the  presence  of  ammonia  could  no  longer  be 
discovered  in  the  filtrate.  The  brown  matter  was  subsequently 
dried,  first  by  exposure  to  the  air  on  the  filter  at  the  ordinaiy 
temperature^  then  at  a  very  gentle  heat^  and  afterwards  by  ex- 
posing it  for  some  time  under  a  bell-glass  to  the  drying  influ- 
ence of  sulphuric  acid. 

As  I  thought  it  more  than  probable  that  the  substance,  from 
the  way  in  which  it  had  been  procured,  contained  some  free 
sulphur  (which  was  afterwards  shown  to  be  the  case),  a  portion 
of  that  which  had  been  so  dried  was  placed  in  a  stoppered  bottle 
and  digested  for  some  days  along  with  bisulphide  of  carbon ;  the 
mixture  was  then  thrown  on  a  filter,  and  washed  with  repeated 
fresh  portions  of  pure  bisulphide  till  but  a  faint  trace  of  residue 
remained  after  the  evaporation  of  a  little  of  the  filtrate;  and  this 
seemed  to  be  due,  not  to  sulphur  as  at  the  first,  but  to  the  brown 
compound  being  soluble  to  a  very  slight  degree  in  the  bisul- 
phide. After  this  treatment  the  bisulphide  was  allowed  to  eva- 
porate off  from  the  substance,  when  it  was  placed  as  before  under 
a  bell-glass  along  with  a  vessel  containing  sulphuric  acid,  where 
it  remained  for  some  days.  Thinking,  however,  that  it  might 
still  not  be  perfectly  dry,  it  was  subsequently  heated  in  a  water- 
bath  or  oven  to  about  212°  F.,  when  I  found  that  a  very  slight 
amount  of  moisture  was  expelled  from  it,  accompanied  by  a  pe- 
culiar sulphurous  smell ;  and  as  soon  as  it  appeared  to  lose  no 
further  weight  by  this  temperature,  it  was  placed  in  a  well-stop- 
pered bottle  and  reserved  for  examination. 

The  substance  so  obtained,  and  in  this  dry  condition,  possesses 
the  following  properties:  it  is  an  amorphous  solid  of  a  light 
brown  earthy  appearance,  is  easily  reducible  to  a  state  of  impal- 
pable powder,  and  has  a  specific  gravity  of  about  1*62.  When 
gently  heated  on  platinum-foil  it  evolves  a  very  peculiar  odour, 
then  blackens,  partially  fuses,  and,  taking  fire,  burns  with  a  pur- 
plish-coloured flame,  emitting  a  faint  odour  of  sulphurous  acid, 
whilst  it  leaves  a  large  carbonaceous  residue,  which  on  the  appli- 
cation of  a  stronger  heat  ignites  and  slowly  burns  away. 

It  is  very  slightly  soluble  in  water,  alcohol,  bisulphide  of  car- 
bon, and  in  ether ,  whilst  it  is  almost  insoluble  in  chloroform 
and  in  benzol.  It  is,  however,  readily  dissolved  by  solutions  of 
the  caustic  alkalies,  and  by  those  of  the  alkaline  cai*bonates  and 
sulphides,  forming  dark  brown  or  reddish-brown  solutions,  from 
which  it  is  again  precipitated,  apparently  unchanged,  by  the  ad- 
dition of  an  acid  in  excess.  It  dissolves  also  in  solutions  of  the 
hydrate  of  lime  and  of  baryta,  and  is  soluble  to  some  extent  in 
alkaline  chlorides  and  iodides. 

As  to  the  action  of  acids,  when  it  was  treated  with  concen- 
trated sulphuric  acid  it  acquired  a  darker  colour,  and  dissolved. 


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260     On  a  very  iingular  Sutphweiied  Nitrogtnow  Compound. 

forming  a  brown  tolution^  which  on  being  heated  became  almost 
black  in  appearance ;  and  this  on  the  addition  of  water  gave  a 
flocculent  dark  brown  precipitate  resembling  the  original  sab* 
stance^  except  in  its  being  of  a  darker  colour. 

Strong  nitric  acid^  even  at  the  ordinary  temperature^  was 
found  to  act  rapidly  on  the  substance^  which  it  oxidises  and  disi 
solves;  but  neither  it  nor  sulphuric  acid  in  a  diluted  condition 
appears  to  exercise  any  effect  on  it  \  for  when  boiled  for  some 
time  with  them  no  apparent  change  was  observed  to  take  place. 
As  to  hydrochloric  acid^  even  when  in  a  tolerably  concentrated 
condition  it  seemed  not  to  produce  any  effect  on  the  substanee 
either  at  the  ordinary  temperature  or  when  boiled  with  it. 

The  compound^  some  of  the  properties  of  which  have  just  been 
noticed^  on  being  submitted  to  analysis  gave  results  which  agree 
most  closely  with  the  formula  C"»  H«*  S*'  N*  0®,  showing  that 
the  substance  is  an  extremely  complex  one^  the  formation  of 
which>  under  the  circumstances  described^  may  be  explained  by 
supposing  the  following  reaction  to  take  place : — 

9(C«HC1«0,H«0)  +  16[(NHVS]+2H«S=C«H«*S«N^0« 

-f"27(NH*Cl)-f"NH»+5S  +  12H«0, 

where  0  equivalents  of  chloral  hydrate^  being  acted  on  by  the 
conjoint  action  of  16  of  sulphide  of  ammonium  and  2  of  hydro- 
sulphuric  acid;  give  rise  to  the  formation  of  I  equivalent  of  the 
brown  compound^  together  with  27  of  chloride  of  ammonium^ 
1  of  ammonia^  5  of  sulphur,  and  12  of  water^  9  of  which  latter 
exist  already  as  constituents  of  the  chloral  hydrate;  and  the  pro- 
bability that  such  changes  do  take  place  appears  to  be  strength- 
ened by  the  fact  that  chloride  of  ammonium^  ammonia,  and  free 
sulphur  were  detected  amongst  the  products  of  the  reaction ;  and 
the  presence  of  a  trace  of  chloroform  may  be  easily  accounted 
for  by  the  action  of  the  free  ammonia  on  a  portion  of  the  un- 
changed chloral  hydrate. 

I  may  observe  that  those  results  as  to  the  composition  of  the 
brown  compound  were  obtained  as  follows : — The  carbon  and 
hydrogen  were  determined  by  combustion  with  chromate  of  lead, 
using  a  long  combustion-tube  and  placing  a  layer  of  copper 
turnings  in  its  anterior  part ;  the  nitrogen  by  burning  with 
soda-lime,  and  estimating  the  resulting  ammonia  by  means  of  the 
chloride  of  platinum;  the  sulphur  by  converting  it  into  sul- 
phuric acid,  which  was  effected  by  treating  the  substance  with 
nitric  acid  and  chlorate  of  potash  (as  recommended  lately  by 
Pearson  for  the  determination  of  sulphur  in  organic  compounds), 
and  then  estimating  the  sulphuric  acid  so  pi*oduced  in  the  usual 
way  by  chloride  of  barium ;  and  lastly  the  oxygen  was  deter- 
mined by  difference  after  the  estimation  of  the  other  constituents. 


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Dr.  A.  SchuBter  on  Unilateral  Conductivity.  361 

But  I  may  remark  that  the  peculiar  properties  and  great  com- 
plexity of  this  compound  offer  considerable  difficulties  in  the 
way  of  an  exact  determination  of  its  different  constituents^  and 
of  its  true  nature  as  a  chemical  combination.  It  appears^  how* 
ever^  from  the  circumstance  that  it  readily  dissolves  in  alkaline 
solutions^  which  then  yield  insoluble  or  sparingly  soluble  dark- 
coloured  precipitates  with  different  metallic  salts,  that  it  partakes 
somewhat  of  the  character  of  an  acid ;  but  this  and  several  other 
obvious  matters  of  inquiry  connected  with  the  compound  are 
subjects  for  further  investigation. 

Before  concluding,  it  is  right  to  state  that,  after  I  had  observed 
many  of  the  facts  which  I  have  here  described,  I  found,  on  look- 
ing over  the  '  Chemical  News/  that  there  was  in  volume  xxv. 
page  87,  a  notice  of  a  communication  *'  On  the  Reaction  of 
Chloral  Hydrate  and  Sulphide  of  Ammonium,''  which  had  been 
read  by  Dr.  J.  Wala  before  the  Lyceum  of  Natural  History  of 
New  York,  in  which  he  notices  some  of  the  changes  which  I 
have  described  as  taking  place  in  that  reaction,  as  well  as  the 
formation  of  a  light-yellow  substance,  the  properties  of  which 
(as  observed  by  him)  do  not  altogether  agree  with  those  of  the 
sulphuretted  compound,  which  I  prepared  in  a  somewhat  differ- 
ent manner  from  that  which  he  adopted.  I  may  also  add  that 
Dr.  Wah  did  not  attempt  to  analyze  the  substance  he  obtained, 
for  want,  as  he  says,  of  material — and  that  he  further  states,  in 
speaking  of  it,  that  0.  Low  asserts  that  in  physical  appearance 
and  chemical  properties  it  resembles  exactly  the  sesquisulphide 
of  carbon  which  he  has  described  in  the  American  Journal  of 
Science,  vol.  xli.  p.  251. 

Be  this  as  it  may  as  regards  the  substance  obtained  by  Dr. 
Walz,  my  analyses  of  the  brown  sulphuretted  compound,  pre- 
pared in  the  manner  stated,  show  that  it  possesses  a  totally  dif- 
ferent chemical  composition  from  the  sulphide  described  by  L5w 
in  the  Journal  to  which  he  has  referred. 


XXXVI.  On  Unilateral  Conductivity. 
By  Arthur  Schuster,  Ph>D.^ 

I.  Introductory, 

WHILE  I  was  engaged  in  other  work  I  met  with  an  irre- 
gularity which  seemed  to  me  to  be  of  such  a  peculiar 
nature  that  I  subjected  it  to  a  separate  investigation.  The 
residts  of  this  investigat'on  have  not  been  entirely  satisfactory. 
I  have  not  been  able  to  raise  the  phenomenon,  to  which  I  allude, 

*  Commimicated  by  the  Author,  having  been  read  in  Section  A.  of  the 
British  Association  at  Belfast  (1874). 


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253  Dr.  A.  Schuster  on  Unilateral  Conductivity* 

above  the  rank  of  an  irregularity ;  that  is  to  8ay>  I  am  not  able 
to  produce  it  at  my  own  will^  although  when  it  is  present  I  am 
generally  able  to  destroy  it.  My  experiments,  however^  leave 
no  doubt  as  to  the  facts^  and  they  show  clearly  that^  in  a  circuit 
composed  entirely  of  copper  wires,  joined  together  by  means  of 
binding-screws^  the  electric  conductivity  may  be  different  in 
opposite  directions.  It  would  be  difficult  to  discover  such  a 
difference  in  the  resistance  by  means  of  the  ordinary  ways  of 
measuring  it.  The  changes  in  the  electromotive  force  of  the 
battery  and  in  the  resistance  of  the  wire^  through  an  alteration 
of  temperature  or  other  accidental  causes^  would  be  sufficient  to 
mask  the  effect.  If  we  use,  however,  the  electromotive  force  of 
a  moving  magnet,  we  are  sure  that  it  is  always  constant  as  long 
as  the  strength  of  the  magnet  does  not  vary  and  the  magnet 
moves  always  between  certain  limits.  A  magnet  rotating  rapidly 
within  a  coil  of  wires  induces  currents  in  alternate  directions  in 
the  coil.  We  are  perfectly  sure  that  the  electromotive  force 
producing  these  currents  is  the  same  in  both  directions ;  and  if 
we  can  detect  any  difference  in  the  strength  of  the  currents 
going  in  opposite  directions  through  the  wire,  we  may  be  sure 
that  only  a  difference  in  the  resistance  can  produce  such  a  result. 
I  have  calculated  the  effect  on  the  galvanometer-needle  of  in- 
duction-shocks following  each  other  in  alternate  directions  at 
regular  intervals  of  time.  If  the  galvanometer  is  provided  with 
a  damping  arrangement,  a  final  condition  will  be  arrived  at  in 
which  the  galvanometer-needle  swings  between  certain  limits. 
These  limits  decrease  as  the  interval  between  the  induction- 
shocks  decreases.  If,  therefore,  the  rotation  of  the  magnet  is 
rapid  enough,  the  effect  of  the  induced  currents  on  the  gidvano- 
meter  ceases  to  be  visible.  It  should,  however,  be  remembered 
that,  although  the  limits  between  which  the  galvanometer-needle 
moves  approach  zero,  the  velocity  of  the  needle  remains  finite. 
This,  of  course,  is  only  true  if  the  two  induction-shocks  are  of 
equal  strength.  If  the  induction-cuiTcnt  in  one  direction  is 
stronger  than  the  current  in  the  opposite  direction,  the  galvano- 
meter will  show  a  permanent  deflection.  As  we  have  two  strong 
currents  balancing  each  other,  a  very  small  difference  in  the 
resistance  will  have  a  strong  effect. 

II.  Description  of  Apparatus. 

The  magnet  which  was  used  as  electromotive  force  was  fixed 
to  the  plate  of  a  siren,  which  could  be  set  into  motion  by  means 
of  a  pair  of  bellows.  The  same  instrument  has  been  formerly 
used  by  R.  Kohlrausch  and  W.  Weber*,  and  later  by  Kohl- 

*  "  Electrodynamic  Measurements,  with  special  reference  to  the  reduc- 
tion of  intensitv  to  absolute  measure,*'  proc.  pf  the  Royal  Saxonian  Society 
of  Sciences,  vol.  iii. 


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Dr.  A.  Schuster  on  Unilateral  Conductivity.  233 

rausch  and  Nippoldt  iu  a  research  on  the  conductivity  of  sulphuric 
acid*.  I  take  the  following  data  from  the  latter  paper.  The 
resistance  of  the  wire  wound  round  the  magnet  is  30  mercury 
unitsf.    The  mean  electromotive  force  of  the  induction-shocks  is 

-^-T  Grove  in  each  direction  if  the  magnet  rotates  n  times  in  a 

second.  During  the  following  investigation  the  magnet  rotated 
about  forty  times  a  second ;  so  that  the  resultant  electromotive 
force  in  each  direction  was  about  0*12  Grove. 

The  resistance  of  the  galvanometer  was  found  to  be  about 
2477  mercury  units ;  so  that  the  resistance  of  the  whole  circuit 
was  as  nearly  as  possible  2500  units.  The  galvanometer  had  a 
plane  mirror,  and  was  read  off  by  means  of  a  telescope  and  scale 
at  a  distance.  In  order  to  have  an  idea  of  the  delicacy  of  the 
instrument,  I  measured  the  deflection  produced  by  a  known 
electromotive  force,  and  I  found  that  the  electromotive  force  of 
TsVir  Daniell  caused  a  first  deflection  of  200*4  divisions  of  the 
scale.  The  whole  arrangement  is  therefore  extremely  simple, 
and  is  represented  by  the  following  diagram  :-^ 


©       <$> 


G  is  the  galvanometer,  I  a  coil  of  wires  within  which  the  rota- 
ting magnet  is  placed. 

III.  Description  of  Experiments. 

When  I  first  joined  the  galvanometer  to  the  inductor  and  ro- 
tated the  magnet,  the  effect  on  the  galvanometer-needle  was  such 
that  I  was  afraid  of  a  bad  contact  either  in  the  galvanometer  or 
in  the  inductor.  The  needle  started  wild  to  one  side,  then 
suddenly  stopped,  turned  back  to  the  opposite  side,  and  moved 
from  one  side  to  another  without  any  law.  The  only  regularity 
I  could  perceive  was  that  it  started  always  in  the  same  direction. 
On  changing  the  wires  leading  to  the  galvanometer,  the  needle 
invariably  started  to  the  opposite  direction.  I  broke  the  con- 
nexions and  left  for  about  two  hours.  When  I  came  back  every 
thing  had  changed.  On  working  the  siren  the  needle  now  went 
slowly  to  one  side,  and  after  a  few  oscillations  came  to  rest  at  a 
point  about  ninety  divisions  of  the  scale  from  the  zero-point. 
On  changing  the  wires  leading  to  the  galvanometer  the  needle 

*  "  On  the  Validity  of  Ohm's  law  for  electrolvtes,  and  a  numeric  deter- 
mination of  the  conductivity  of  sulphuric  acid.  Poffff.  Ann,  vol.  cxxxviii. 
p.  379  (1869). 

t  All  resistances  in  this  research  are  referred  to  mercury  units. 


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254  Dr.  A.  Schuster  on  Unilateral  Conductivity. 

went  to  the  other  side,  and  the  permanent  deflection  was  nume- 
rically the  same*  The  same  experiment  was  repeated  several 
times,  and  the  same  deflection  was  always  observed.  While 
thinking  over  this  result,  I  took  the  apparatus  to  pieces,  t. «« 
disconnected  all  wires  and  joined  them  again  together.  The 
effect  had  now  entirely  disappeared,  the  needle  coming  to  rest 
exactly  at  its  sero-point*  The  next  dav  a  small  unilateral  con- 
ductivity (as  the  raect  may  be  properly  called)  was  observed, 
but  after  a  few  experiments  disappeared  again.  During  several 
days  I  found  that  this  unilateral  conductivity  generally  appeared 
when  the  wires  had  had  some  rest ;  and  I  therefore  joined  into 
the  circuit  different  wires  which  had  not  been  used  for  some 
time.  Some  of  these  wires  showed  the  effect,  and  some  did  not ; 
in  all  cases  it  disappeared  after  several  experiments.  A  wire 
which  had  never  been  used  before  showed  the  effect  in  a  remark- 
able degree.  The  introduction  of  this  wire,  which  could  not 
have  a  resistance  larger  than  0*1  unit,  was  sufficient  to  drive 
the  needle  wild  to  one  side.  I  must  mention  here  a  remarkable 
fact.  Suppose  we  have  a  circuit  in  its  normal  state  (that  is, 
showing  no  unilateral  conductivity) ;  let  us  introduce  a  wire,  and 
suppose  that  the  unilateral  conductivity  is  now  observed.  Take 
the  wire  out  again,  so  that  the  circuit  is  exactly  the  same  as  it 
was  before  when  no  unilateral  conductivity  existed.  The  uni- 
lateral conductivity  will  now  appear,  generally  even  in  the  same 
degree  as  it  did  with  the  new  wire.  If  we  now  by  experimenting 
destroy  the  unilateral  conductivity  and  join  the  wire  which  had 
caused  the  disturbance  into  the  circuit  again,  it  will  generally 
behave  quite  neutral ;  t.  e,  no  unilateral  conductivity  wUl  be  ob- 
served. If  it  do  not  behave  quite  neutral,  it  will  only  show  a 
small  unilateral  conductivity,  which  will  be  destroyed  by  a  second 
or  third  experiment  of  the  same  kind. 

IV.  Proposed  Theory  of  the  Phenomenon. 

It  is  chiefly  the  remarkable  fact  just  described  (as  well  as  the 
previous  observation,  that  generally  new  wires,  or  such  wires  as 
have  not  been  used  for  some  time,  showed  the  effect)  that  has 
led  me  to  a  theory  which,  although  proved  afterwards  to  be,  if 
not  erroneous,  at  any  rate  incomplete,  explains  so  well  many  of 
the  most  startling  observations  that  I  think  it  welt  to  give  it 
here.  Supposing  we  pass  an  electric  spark  from  a  sphere  to  a 
point,  it  is  known  that  the  distance  the  electric  spark  will  pass 
for  a  given  electromotive  force  is  different  according  as  the  sphere 
is  positively  or  negatively  electrified.  A  circuit  composed  of  a 
metallic  wire,  terminated  at  one  end  by  a  sphere,  separated  by  a 
thin  layer  of  air  from  the  other  end  of  the  wire  would  therefore 
show  unilateral  conductivity,  the  positive  electricity  passing  more 


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Dr.  A.  Schuster  on  Unilateral  Conductivity.  255 

easy  in  one  direction  through  the  air  than  in  the  other.  It  is 
also  known  that  metals  condense  air  in  great  quantity  at  their 
surface ;  and  if  we  screw  two  wires  with  their  condensed  air  to* 
gether,  it  is  quite  conceivable  that  particles  of  air  will  separate 
the  two  surfaces  of  copper^  and  that  a  small  voltaic  arc  will  there- 
fore be  formed.  Unilateral  conductivity  would  be  the  result. 
If  we  screw  a  wire  which  has  air  condensed  on  its  surface  to  a 
binding-screw^  part  of  the  air  will  pass  from  the  wire  to  the 
binding-screw ;  and  it  would  thus  be  explained  that  the  tempo* 
rary  addition  of  a  new  wire  may  produce  a  unilateral  conductivity 
in  a  circuit  which  has  not  shown  it  before, 

V.  Experiments  confirming  the  Theory. 

Many  minor  coincidences  seemed  to  confirm  this  theory* 
Cleaning  the  ends  of  the  wire  with  the  knife  generally  destroyed 
the  effect.  It  was,  as  a  rule,  observed  in  those  parts  of  the  cir- 
cuit which  had  been  disconnected  over  night.  It  is  always  easy 
to  find  out  in  what  part  of  the  circuit  the  effect  has  its  seat. 
We  have  only  to  change  the  connexions  in  various  places,  and 
to  observe  in  what  direction  the  needle  is  deflected.  I  mention 
one  particular  case. 

The  rotation  of  the  magnet  one  day  caused  a  permanent  de- 
flection of  the  needle  of  295  divisions  of  the  scale.  On  reversing 
the  wires  at  the  ends  of  the  induction-coil,  the  needle  was  de- 
flected towards  the  other  side.  The  effect,  therefore,  had  its 
seat  in  the  induction-coil.  The  coil  was  divided  into  two  halves, 
which  were  connected  by  means  of  a  stout  copper  wire  about 
half  an  inch  in  length.  I  remembered  that  this  piece  of  wire 
had  been  exposed  to  the  air  over  night,  and  I  therefore  reversed 
the  wire ;  the  needle  was  deflected  295  divisions  of  the  scale  to 
the  other  side,  showing  that  my  supposition  had  been  correct, 
and  that  this  small  piece  of  wire,  the  resistance  of  which  may 
have  been  about  the  hundred-thousandth  part  of  the  whole 
resistance,  had  caused  the  deflection.  On  reversing  the  wire 
again,  the  effect  had  disappeared. 

Another  wire  was  now  taken  to  join  the  two  halves  of  the  in- 
duction-coil ;  a  permanent  deflection  of  about  80  divisions  of 
the  scale  was  observed.  On  cleaning  the  ends  of  the  wire  with 
a  knife  the  effect  disappeared. 

These  experiments  seemed  alone  sufficient  to  prove  the  theory. 
In  order,  however,  to  subject  it  to  a  severer  test,  I  thought  of 
condensing  air  artificially  on  the  surface  of  the  wire.  This  can 
readily  be  done  by  means  of  powdered  charcoal,  which,  as  is 
known,  absorbs  air  in  great  quantity.  A  wire  which  was  in  its 
normal  state  was  therefore  laid  with  one  end  into  powdered 
charcoal  for  about  five  minutes.    When  reintroduced  into  the 


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256  Dr.  A.  Schuster  on  Unilateral  Conductivity. 

circuit,  the  wire  showed  a  very  strong  unilateral  conductivity. 
Cleaning  and  scraping  the  wire  had  at  first  apparently  no  effect ; 
screwing  the  wire^  however,  to  another  binding-screw  attached 
to  the  induction-coil  destroyed  the  effect  entirely,  so  that  the 
wire,  even  when  screwed  to  the  original  binding-screw,  showed 
no  unilateral  conductivity.  The  same  experiment  was  repeated 
a  second  time,  and  with  the  same  result.  Five  minutes'  lying 
in  powdered  charcoal  was  sufficient  to  reproduce  a  strong 
unilateral  conductivity;  and  the  same  operation  as  before 
destroyed  it. 

VI.  Failure  of  the  Theory. 

A  third  trial  to  obtain  unilateral  conductivity  by  the  same 
means  failed.  The  wire  was  put  into  the  charcoal  for  several 
hours  instead  of  several  minutes ;  but  even  then  it  remained  in 
its  neutral  state.  All  the  various  circumstances  which  generally 
had  produced  unilateral  conductivity  were  now  tried;  but  none 
succeeded.  New  wires  were  tried;  the  whole  apparatus  was 
left  untouched  and  disconnected  for  several  days ;  but  I  could 
not  obtain  the  effect  again.  I  used  the  same  instrument  in 
another  investigation  during  three  consecutive  weeks,  during 
which  various  new  wires  were  tried  and  new  combinations  em- 
ployed ;  but  the  effect  only  came  out  once  more,  and  this  time 
m  the  galvanometer.  The  deflection  amounted  to  about  20 
divisions  of  the  scale.  It  lasted  for  several  days  and  then  dis- 
appeared. 

VII.  Relation  of  unilateral  conductivity  to  previously  known 
phenomena. 

It  is  perhaps  worth  while  to  ^ay  a  few  words  about  the  rela- 
tion in  which  the  phenomenon  described  in  these  pages  stands' 
to  other  phenomena  to  which  a  similar  name  has  sometimes  been 
given.  Before  attempting  to  do  this,  however,  it  is  necessary 
to  allude  to  one  or  two  objections  which  might  be  raised  against 
my  interpretation  of  the  experiments  described  above. 

Can  the  experiments  be  explained  by  thermoelectric  currents 
set  up  by  the  heating  of  the  wire  through  the  electric  vibra- 
tions f  I  think  that  a  careful  perusal  of  the  experiments  will 
convince  everybody  that  they  cannot  be  explained  that  way.  I 
need  only  draw  attention  to  the  unstableness  of  the  effects  and 
to  the  different  facts  upon  which  I  thought  myself  justified  in 
founding  the  theory  mentioned  above.  These  facts  certainly 
cannot  be  explained  by  thermoelectric  currents. 

At  first  sight  my  experiments  seem  to  have  some  relation  to 
a  class  of  phenomena  discovered  by  Poggendorff*^,  and  described 

♦  Annalen,  vol.  xlv.  p.  353  (1838),  vol.  liv.  p.  192  (1841). 

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Dr.  A.  Schuster  on  Unilateral  Conductivity.  257 

by  him  under  the  name  of  bilateral  deflection  {doppelsinnige 
Ablenkunff),  It  seems  that  the  currents  in  alternate  direction 
affect  to  a  certain  degree  the  temporary  magnetization  of  the 
needle.  This  has  of  course  an  influence  on  the  time  of  vibra-* 
tion,  which  is  shorter  while  the  current  increasing  the  mag* 
netism  passes  through  the  galvanometer.  While  the  current 
passes  in  this  direction  the  needle  makes  a  greater  way  than  in 
the  same  time  while  the  current  in  the  opposite  direction  is 
passing.  The  two  currents  succeeding  each  other  at  regular 
mtenrals  of  time  will  therefore  not  counterbalance  each  other^ 
but  the  current  increasing  the  magnetism  of  the  needle  will  have 
the  upper  hand. 

The  result  will  be  that  the  needle  will  be  driven  towards  the 
side  to  which  it  was  originally  deflected.  This^  of  course^  only 
happens  if  the  effect  of  this  magnetization  is  sufficiently  strong 
— that  is  to  say^  if  the  original  deflection  is  sufficiently  large ; 
for  the  magnetizing  effect  on  a  needle^  placed  at  right  angles  to 
the  axis  of  the  galvanometer-coil^  is  zero^  and  increases  as  the 
sine  of  the  angle  of  deflection.  According  to  Poggendorff, 
a  needle  which  is  not  deflected  more  than  eight  or  ten  degrees 
from  its  zero-pointy  will  return  to  that  point  if  currents  in  alter- 
nate directions  are  sent  through  the  galvanometer.  If,  how- 
ever^ the  original  deflection  is  greater  than  10  degrees,  the 
needle  is  driven  violently  towards  the  side  of  this  deflection. 

It  is  evident  that  this  effect  of  the  electric  vibrations  is  a 
function  merely  of  the  position  of  the  needle ;  altering  the  con- 
nexions could  therefore  never  produce  a  reversal  of  the  effect. 
As,  however,  I  could  always  drive  the  needle  towards  the  other 
side  by  suitably  changing  the  connexions,  this  bilateral  deflec- 
tion has  evidently  had  nothing  to  do  with  the  abpve  experi- 
ments. 

It  remains  to  say  a  few  words  about  what  has  been  called 
unipolar  conductivity.  This  unipolar  conductivity  has  been  ob- 
served in  electrolysis  and  in  flames.  The  unipolar  conductivity 
in  electrolytes  has  been  explained  by  secondary  influences  of 
electrolysis',  and,  therefore,  does  not  stand  in  any  relation  to 
what  I  have  called  unilateral  conductivity.  The  unipolar  conduc- 
tivity of  flames  has  not  yet  been  satisfactorily  explained.  If  my 
supposition  is  correct,  and  if  we  must  look  to  the  air  condensed 
on  the  surface  of  the  wires  for  the  explanation  of  unilateral  con- 
ductivity, it  will  most  likely  prove  to  be  closely  allied  to  the 
unipolar  conductivity  of  flames. 

VIIL  Conclusion, 

The  result  of  the  foregoing  investigation  may  be  perhaps  best, 
stated  as  follows  *^— * 

Phil.  Moff.  S.  4.  Vol.  48.  No.  818.  Oct.  1874.  S 


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258  Lord  Baykigh  tm  the  VHrMHam  of 

The  current  produced  by  an  eledramotive  force  m  a  circuit 
compoeed  entirely  of  copper  wiree  joined  together  by  maosf  of 
Unding^ecrewi  may,  under  certain  eircumttancet,  be  different  frmn 
the  current  produced  by  the  eame  electromotive  force  acting  in  the 
opposite  direction. 

I  have  called  this  phenomenon  "  unilateral  condnetirity;^  and 
I  have  tried  to  bring  it  into  connexion  with  known  facts.  Hie 
most  plausible  explanation  seemed  to  me  to  be^  that  a  thin  layer 
of  air  may  sometimes  intervene  between  the  two  wires  which 
are  screwed  together.  This  explanation  has  been  confirmed  by 
some  experiments.  Other  experiments  have  shown  that  the  ex* 
planation  is  insufficient.  I  do  not  think  that  the  evidence  is 
sufficiently  strong  to  abandon  altogether  an  explanation  which 
seems  to  agree  so  well  with  the  most  characteristic  features  of 
the  phenomenon.  Secondary  causes  may  intervene  which  pre* 
vent  the  phenomenon  from  being  formed.  I  suggest  the  dif- 
fusion of  the  gases  into  the  wires  as  such  a  secondary  pheno- 
menon. E£Fects  which  are  so  unstable,  however,  are  never 
explained  by  a  simple  set  of  experiments.  They  will  only  be 
satisfactorily  explained  by  a  number  of  observations  from  dif- 
ferent experimenters.  It  is,  I  hope,  a  sufficient  justification  for 
the  publication  of  the  above  experiments  if  they  draw  the  atten* 
tion  of  physicists  to  a  class  of  pnenomena  which  sometimes  may 
seriously  interfere  with  their  measurements. 


XXXYU.  On  the  Vibrations  of  Approximately  Simple  Systems. 
By  LoKD  Batleigh,  M.A.,  F.H.S.'^ 

IN  a  paper  with  the  above  title,  published  in  the  Philosophieal 
Magazine  for  November  1873, 1  drew  attention  to  the  fact 
that  when  the  natural  vibrations  of  a  system  are  thoroughly 
known,  the  effect  of  a  small  variation  in  the  system  in  changing 
the  types  and  periods  of  vibration  may  be  readily  calculated  by 
a  general  method.  In  particular  I  proved  that  the  altered  pe- 
riods may  be  found  from  the  new  values  of  the  potential  and 
kinetic  energies  on  the  hypothesis  that  the  types  are  unchanged, 
subject  to  an  error  of  the  second  order  only.  The  present  note 
shows  how  a  farther  approximation  may  be  made,  and  how  a 
similar  method  may  be  applied  to  a  system  subject  to  small  dis- 
sipative  forces. 

If  ^p  ^^  &c.  be  the  normal  coordinates  of  the  original  system, 
the  expressions  for  the  kinetic  and  potential  energies  are 

T=i[l]*?+4[2]^i+ 

*  Communicated  by  the  Author. 


•  •  •  >T 

f  ....  (1) 


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(2) 


Jfproximaiefy  Single  Syiiems.  259 

Now  let  the  system  be  dightly  varied,  so  that  T  and  Y  become 

T+CT=i([ll  +S[1])^!+  . . .  +8[12]^i^,+  •  •  • . 

V+8V=i({l}  +  8{l}>I+...+8{12}^i^,+  ..., 
giving  for  the  equations  of  vibration  of  the  altered  system 

+  ...=0, 

(S[12]D«+8{12}>i  +  ([2]D«H.8[a]D«+{2}  +  8{2}>« 

+  ...=0, 

&c. 
In  the  original  system  one  of  the  natural  vibrations  is  that 
denoted  by  the  sole  variation  of  if>^.  In  the  altered  system  this 
will  be  accompanied  by  simultaneous  small  variations  of  the 
other  coordinates.  If  the  whole  motion  vary  as  cos  Pft,  we  get 
from  the  sth  equation,  as  was  proved  in  the  paper  referred  to, 

an  equation  which  may  be  regarded  as  determining  approximately 
the  character  of  the  altered  types  of  vibration. 
Now  the  rth  equation  of  (2)  gives 
i/>r(-/>J[r]-pj8[r]  +  {r}+8{f})  +  .-.  +  ^.(-p;8M 

+  8{r*}>+...=0.      (4^ 

Using  in  (4)  the  values  of  <f>t :  ^^  given  in  (3),  we  get  for  the 
value  ofjE>Jj^ 

'     „«-  M  +  8{r}        (;>;gW-8{r.}X     .     .    (g) 

'''     [r].+  S[r]  [r]M{/»;-i>;) 

in  which  the  summation  extends  to  all  values  of  $  other  than  r. 
The  first  term  in  (5)  gives  the  value  of  fl  calculated  withoujt 
allowance  for  the  change  of  type,  and  is  sufficient  when  the  square 
of  the  alteration  in  the  system  may  be  neglected.  If  pr  f^^r  to 
the  gravest  tone.of  the  system,  pi— pi  is  always  positive,  and  the 
term  of  the  second  order  in  (5)  is  negative,  showing  that  the 
calculation  founded  on  the  unaltered  type  gives  in  this  case  a 
result  which  is  necessarily  too  high. 

If  obly  the  kiiietic  energy  undergo  variation, 

w 


S2 


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(8) 


260  Lord  Rayleigh  on  the  Vibrations  of 

As  an  example  we  may  take  a  uniform  string  of  length  /  and 
density  p,  carrying  a  small  toad  m  at  its  middle  point.  If  y  be 
the  transverse  displacement  at  point  x, 

the  origin  of  x  being  at  one  end.  In  this  case  for  the  gravest 
tone  we  have 

8T=im(<^',-(^8+^5-...)S 
so  that 

Accordingly 

since  pjjpj— pj=l  :«*— 1. 

Fr  here  denotes  the  value  of/),,  when  there  is  no  load. 
Now 

«*— 1       *— 1       *+l 
in  which  the  values  of  s  are  3,  5^  7>  9>  &c.    Accordingly 

■^zTi^'i*  •  •   .^  •   •  •  •  (y) 

and  therefore 

pJ=P»{l-^  +  ^'  +  cube«},      .    .    (10) 

which  gives  the  pitch  accurately  as  far  as  the  square  of  the  ratio 
m:lp, 

l^e  free  vibrations  of  a  svstem  subject  to  dissipation-forces  are 
determined  in  general  by  the  equations 

^#-1-^-'  •  •  •  •  <") 

where\  T  and  V  are  as  before^  and  F,  called  the  dissipation-func- 
t^n,  is  of  the  form 

*  See  ft  paper  "  On  lonie  General  Tlieorcms  relating  to  Vibrations," 
Mathematical  Society's  Proceedings^  June  1873. 


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Approximately  Simpk  Systems^  261 

3y  a  suitable  transfcHrmation  any  two  of  the  functions  T,  P,  V 
can  be  reduced  to  a  sum  of  squares^  but  not  in  general  all  three. 
When  all  three  occur^  the  types  of  vibration  are  more  complicated 
than  those  of  a  conservative  system,  or  of  that  of  a  dissipative 
system  with  one  degree  of  freedom.  When,  however,  the  fric- 
tional  forces  are  small,  as  in  many  important  applications  they 
are,  it  is  advantageous  to  proceed  as  if  the  system  were  conser- 
vative, and  reduce  T  and  V  to  sums  of  squares,  leaving  F  to  take 
its  chance.     In  this  way  we  obtain  equations  of  the  form 

in  which  the  coefficients  (11),  (22),  (12),  &c.  arc  to  be  treated 
as  small. 

Let  the  type  of  vibration  considered  be  that  which  differs  little 
from  the  sole  variation  of  ^,.,  and  let  all  the  coordinates  vary  as 
c'r',  where  pr  will  be  complex,  as  also  the  ratios  of  the  coor* 
dinates.     From  the  ^  equation^ 

(fM  +  {*}>.+  (^*)pA+  •  • .  =0, 

we  get,  by  neglecting  the  terms  of  the  second  order, 

^''^^    w^^wv  '  •  •  *  ^  ^ 

which  determines  the  alteration  of  type.  Although  p  is  com- 
plex, the  real  part  is  small  compared  with  the  imaginary  part ; 
and  therefore  (14)  indicates  that  the  coordinates  ^,  have  appi*oxi«> 
mately  the  same  phase,  and  that  phase  a  quarter  period  different 
from  that  of  ^y.     The  rth  equation  gives,  by  use  of  (14), 

i';W+{r}+(rK-2-^|^=0,     .     .      (15) 

from  which  it  appears  that^^r  may  be  calculated  approximately 
from  the  equation 

ir-\p\-\-{r)Pr+\r)=0;     ....      (16) 

that  is,  as  if  there  were  no  change  in  the  type  of  vibration.  The 
rate  at  which  the  motion  subsides  will  not  be  altered,  even  though 
the  terms  of  the  second  order  in  (15)  be  retained. 

The  reader  mav  apply  these  formulse  to  the  case  of  a  uniform 
string  whose  middle  point  is  subject  to  a  small  retarding  force 
proportional  to  the  velocity. 

It  is  scarcely  necessary  to  point  out  that  these  methods  apply 
to  other  physical  problems  than  those  relating  to  the  vibrations 


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262  Mr.  W.  B.  Davis  an  m  Mtthdd  oflUiairaiing 

of  materitl  syttemt*  For  the  free  motioii  of  heat  in  a  eondoetor^ 
we  obtain  equations  eorresponding  to  those  of  materisl  systona 
which  are  supposed  to  be  devoid  of  inertia«  The  funetioiiB  F  and 
y  may  thus  be  reduced  to  sums  of  squares ;  and  the  effect  of  a 
small  variation  in  the  system  may  be  investigated  by  methods 
parsllel  to  those  employdl  in  the  present  paper. 

TerKng  Pbce»  Withsm, 
September  11, 1874. 


XXXVIIL  On  a  simple  Method  of  Illustrating  the  chief  Pheno- 
tnena  of  Wave-Motion  by  means  of  Flexible  Otris.  By  the  late 
W.  S.  Davis,  FJt.A.S.^  Derby*. 

[VTith  a  Plste.J 

THE  simple  methods  about  to  be  described,  of  exhibiting  the 
chief  phenomena  of  wave-motion,  were  suggested  during 
some  experiments  lately  made  by  the  author  on  the  refraction  of 
liquid  waves  t*  These  experiments  consisted  in  the  production 
of  waves  on  the  surfaces  of  two  liquids  of  different  densities, 
lying  side  by  side :  on  agitating  the  surface  of  either  liquid, 
waves  were  produced  whicn  passed  from  one  liquid  to  the  other, 
at  the  same  time  undergoing  changes  in  amplitude,  lengthy  and 
form  of  front.  In  preparing  diagrams  to  represent  these  phe- 
nomena it  became  necessary  to  make  drawings  of  vertical  sec* 
tions  through  the  two  liquids,  perpendicular  to  their  line  of 
separation. 

The  appearance  presented  by  the  sinuous  lines  on  these  dia« 
grams  immediately  suggested  that  a  similar  appearance  could  be 
exhibited  by  means  of  waves  on  flexible  ooras.  India-rubber 
tubes,  variously  suspended,  and  both  empty  and  loaded,  were 
tried  without  satisfactory  success ;  the  waves  moved  too  quickly 
to  be  well  observed,  and  the  reflected  waves  interfered  with  the 
direct  cfne^.  Further  experiments  led  the  author  to  devise  the 
simple  apparatus  now  exhibited,  which,  however,  has  been  made 
to  serve  for  many  other  illustrations  of  wave-motion  in  addition 
to  those  it  was  at  first  intended  to  show. 

The  apparatus  consists  essentially  of: — (1)  a  piece  of  stout 
board  about  20  feet  long  and  9  inches  wide,  which  should  be 

Cted  black;  and  (2)  three  or  four  ropes,  which  must  be  both 
y  and  flexible :  the  ropes  used  by  builders  for  securing  their 
sctffibldiDg  have  been  found  to  answer  very  well^  especially  if 
they  have  been  in  use  some  time.     To  enable  the  eye  to  readily 

♦  Read  before  the  Physical  Society,  May  9,  1874.    Commumcated  by 
the  Society, 
t  Bee  Brit.  Assoc.  Report,  1873. 


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Phenomena  of  JFwe^MoHon  by  memo  of  Flexible  Ccrde^    d63 

distinguish  any  ptrtieolar  rope  when  two  or  more  are  used 
together^  it  is  well  to  coyer  the  ropes  with  di£ferently  coloured 
fabrics^  say  red^  bluci  and  green.  A  few  other  accessories  are 
necessary^  which  will  be  described  as  they  are  required* 

By  means  of  this  apparatus  wares  may  be  produced  which 
more  slowly  enough  to  be  readily  examined  by  the  eye.  The 
chief  phenomena  of  wave-motion  which  can  oe  shown  are  as 
follows  :— 

1.  TroMsmiseion  of  a  Wave. — One  end  of  a  rope^  a  few  feet 
longer  than  the  boards  is  fixed  to  a  hook  at  the  end  of  the  board. 
The  free  end  of  the  rope  is  then  taken  in  the  hand^  and^  the 
the  rope  being  quite  slacks  a  sudden  up-and-down  movement  of 
the  hand  is  made.  A  protuberance  is  thus  formed  which  moves 
very  slowly  along  the  rope,  presenting  the  appearance  shown  in 
Plate  y.  fig.  1* 

A  single  up-and-down  movement  produces  a  wave  consisting 
of  a  crest  only,  the  trough  being  suppressed  by  the  board ;  if, 
however,  with  the  rope  very  slack,  the  hand  be  moved  up  and 
down  very  quickly  and  energetically,  a  series  of  waves,  consisting 
of  both  crest  and  trough,  are  produced  (fig.  2). 

2.  Amplitude  and  Wave-length. — Waves  having  any  length, 
from  1  to  6  or  7  feet,  and  amplitudes  of  similar  dimensions,  are 
easily  produced  by  properly  controlling  the  rapidity  and  energy 
t)f  the  motion  of  the  hand. 

8.  Decrease  of  Intensity  with  Dietance. — ^This  is  illustrated  by 
a  succession  of  waves  produced  by  the  well-timed  motion  of  the 
hand  (fig.  2).  The  actual  decrease  of  amplitude  in  this  case  is, 
of  course,  due  to  the  loss  of  energy  by  friction,  and  not  to  lateral 
-spreading. 

4.  Relation  of  Velocity  to  Elasticity, — Two  similar  ropes,  one 
covered  with  red  and  the  other  with  blue,  are  laid  side  by  side 
along  the  board  and  fastened  to  hooks  at  one  end.  The  free 
ends  of  the  ropes  are  held  in  the  hand,  with  the  finger  between 
them,  and,  care  being  taken  that  they  are  equally  loose,  the  hand 
is  moved  up  and  down  as  usual.  The  result  is  that  a  wave  of 
the  same  height  and  length  is  produced  on  each  rope,  and  the 
two  waves  travel  side  by  side  to  the  ends  of  the  ropes.  The  ex- 
periment is  repeated  with  one  rope  somewhat  tighter  than  the 
other,  when  the  wave  on  the  tighter  rope  is  observed  to  travel 
faster  than  that  on  the  looser  one  (fig.  3).  On  continuing  to 
tighten  the  rope  the  velocity  of  the  wave  is  more  and  more  in- 
creased, and  may  be  caused  to  reach  the  end  of  the  rope  a  whole 
length  or  more  before  its  fellow. 

5.  Relation  of  Velocity  to  Density, — ^To  exhibit  this  relation  a 

*  The  length  of  the  board  in  the  figures  \b  drawn  to  a  much  smaller 
'scale  than  the  other  parts. 


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264    ,       Mr.  W.  S.  Davis  an  a  Method  of  lUuUrating 

loaded  rope  is  required.  That  now  used  has  strung  upon  it  m 
number  of  rings  of  lead  cut  from  a  leaden  water-pipe;  these 
are  placed  about  6  inches  apart,  and  are  covered  with  india- 
rubber  bands  to  prevent  their  making  unpleasant  noise.  IW 
loaded  and  an  unloaded  rope  are  laid  on  the  board  side  by  side, 
and  fixed  at  one  end.  Then^  taking  care  the  tension  is  equal 
in  the  two  ropes,  waves  are  simultaneously  generated  on  theroi 
as  before  described.  It  is  then  observed  that  the  wave  on  the 
loaded  rope  lags  considerably  behind  the  other  (fig.  4).  By  suffi- 
ciently tightening  the  loaded  rope  the  velocity  of  its  waves  may 
be  made  equal  to,  or  even  greater  than  that  of  the  waves  of  tl^ 
unloaded  rope.  This  may  be  used  to  explain  whv  the  velocity 
of  sound  in  water  is  greater  than  in  the  much  less  oense  medium^ 
air. 

6.  Transmission  of  Waves  from  one  Medium  to  another  of  dif- 
ferent Density. — The  loaded  cord  is  attached  end  to  end  to  one 
much  lighter  than  itself;  the  united  cords  are  laid  on  the  board 
with  the  splice  at  about  the  middle  of  its  length.  Then,  fasten- 
ing the  end  of  the  lighter  cord,  waves  are  generated  on  the 
heavier  one.  These  waves  pass  onwards  to  the  lighter  cord,  on 
reaching  which  they  acquu*e  greater  amplitude,  velocity,,  and 
length  (fig.  6).  If  the  heavier  cord  be  fixe4  and  waves  be  gene- 
rated on  the  lighter  one,  the  reverse  changes  to  those  just  stated 
occur  on  the  waves  reaching  the  heavier  cord.  It  is  an  interest- 
ing experiment  to  transmit  waves  along  a  succession  of  three  or 
more  cords  alternately  heavy  and  light.  With  three  cords  joined 
end  to  end,  the  middle  one  being  heavier  than  the  others,  a  good 
illustration  is  produced  of  the  changes  of  velocity,  length,  and 
amplitude  which  setherial  waves  unaergo  in  passing  perpendi- 
cularly through  a  medium  with  parallel  faces. 

7.  Separation  of  a  Wave  into  two  or  more  smaller  Waves. — A 
single  cord  extending  half  the  length  of  the  board  is  joined  to  a 
double  one  extending  the  other  half.  Waves  are  transmitted 
from  the  single  cord  to  the  double  one ;  on  reaching  the  latter 
each  wave  divides  in  two,  one  wave  traversing  one  part  of  the 
double  cord,  and  the  other  wave  the  other  part.  By  giving  each 
part  of  the  double  cord  a  different  tension,  the  velocity  of  the 
waves  will  be  different  in  each  (fig.  6).  The  waves  on  the  double 
cord  may  be  made  to  move  in  planes  at  right  angles  to  each 
other  by  the  use  of  proper  guides,  thus  furnishing  an  illustration 
of  some  of  the  phenomena  of  double  refraction. 

8.  Superposition  and  Interference. ^The  same  arrangement  is 
used  as  in  7,  but  the  waves  are  transmitted  from  the  double 
cord  to  the  single  one.  With  equal  tension  in  each  part  of  the 
double  cord,  the  waves  simultaneotusly  produced  on  each  part  run 
side  by  side  until  they  enter  the  single  cord^  when  they  are  su- 


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Phenomena  of  Wave-motion  by  iheans  ofFUiXiible  Cords.    265 

perposed  and  produce  a  wave  of  doable  amplitude.  One  half  of 
the  double  cord  may  be  tightened  until  its  wave  reaches  the  single 
cord  half  a  wavers  length  before  the  wave  on  the  other  half ^ 
when  interference  occurs^  there  being  little  or  no  lateral  motion 
to  be  observed  in  the  single  cord. 

-  9.  Plane  of  Waves, — In  the  experiments  previously  described 
the  waves  were  transmitted  in  a  vertical  plane ;  but  by  properly 
directing  the  motion  of  the  hand,  the  waves  may  be  transmitted 
in  planes  variously  inclined  to  the  board,  or  in  a  plane  parallel 
with  it.  Waves  in  space  of  three  dimensions,  corresponding  to 
circularly  polarized  light,  are  produced  by  rapidly  and  regularly 
moving  the  hand  in  a  circle,  the  cord  then  taldng  the  form 
shown  at  the  right  of  figs.  7  and  9. 

10.  Polarization. — A  series  of  flat  boards  are  used  as  guides; 
which  are  clamped  on  the  long  board.  These  are  shown  in 
figs.  7,  8,  9.  The  vertical  and  oblique  guides  are  each  in  two 
pieces,  which  are  so  approximated  to  each  other  as  to  just  allow 
the  cord  to  move  freely  between  them.  The  horizontal  guide  is 
in  one  piece  only.  The  vertical  and  horizontal  guides  being 
fixed  as  shown  in  figs.  7  and  8,  waves  in  a  vertical  plane  are 
transmitted  from  that  end  of  the  rope  nearest  the  vertical  guides ; 
the  waves  then  pass  freelv  through  the  vertical  guides^  but  are 
completely  stopped  by  the  horizontal  one.  Waves  in  a  hori« 
zontal  plane  transmitted  from  the  other  end  of  the  apparatus 
pass  the  horizontal  guide,  but  are  stopped  by  the  vertical  ones 
(fig.  8).  Waves  in  an  oblique  plane  transmitted  from  either  end 
are  resolved  by  the  nearest  guide  into  a  component  in  its  own 
plane  and  a  component  at  right  angles  which  is  suppressed; 
the  former  passes  on  and  is  stopped  by  the  next  guide.  Circularly 
polarized  waves  on  reaching  the  guides  are  similarly  resolved 
(fig.  7).  , 

11.  Depolarization, — A  pair  of  oblique  guides  are  required  in 
addition  to  those  described  in  10.  The  arrangement  of  these  is 
shown  in  fig.  9,  which  needs  no  further  explanation.  The  waves 
are  supposed  to  proceed  from  right  to  left.  With  a  single  cord 
as  in  fig.  9,  or  with  a  partly  double  one  as  in  fig.  6,  an  endless 
variation  of  experiments  relating  to  polarization  maybe  produced. 

12.  Radiation  and  Absorption. — ^A  rod  of  iron  about  2  feet 
in  length,  having  an  eye  at  the  centre  and  at  each  end,  is  fixed 
by  means  of  a  screw  or  pin  through  the  central  eye  to  an  up* 
nght  support  of  wood  clamped  at  about  the  middle  of  the  board 
(fig.  10).  The  iron  rod  must  be  able  to  rotate  freely  about  the 
pin  in  a  vertical  plane  parallel  to  the  board,  but  in  no  other 
plane.  Attaching  a  cord  to  one  end  of  the  iron  rod  and  conti-^ 
nuing  it  to  the  end  of  the  board,  a  series  of  properly  timed  waves 
are  sent  fdOPg  itj  when  the  rod  vibrates  in  synchronisni  with  th^ 


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waves.  If  a  second  cord  be  attached  to  the  other  end  of  the 
rod  and  waves  be  transmitted  as  before^  the  vibrations  of  the 
rod  set  up  waves  in  this  cord  which  correqKmd  in  period  and 
length  to  those  on  the  first  cord^  thus  furnishing  an  illustration 
of  the  reciprocity  of  radiation  and  absorption. 

The  autnor  has  reason  to  think  that,  as  nearly  all  the  above- 
described  illustrations  have  been  devised  during  the  last  twdve 
months,  the  method  is  capable  of  much  further  development  and 
greater  perfection. 

XXXIX.  Researches  in  Acoustics. — ^No.  V.* 
By  Alfred  M.  MATKRf* 

1.  An  Experimental  Confirmation  of  Fourier's  Theorem  as  ap^ 
plied  to  the  Decomposition  of  the  Vibrations  of  a  Comporiie 
Sonorous  Wave  into  its  elementary  Pendulum^vtlfrations^ 

A  SIMPLE  sound  is  a  sound  which  has  only  one  pitch.  Such 
a  sound  is  produced  when^  with  a  bow,  we  gently  vibrate  the 
prongs  of  a  tuning-fork  and  bring  them  near  a  cavity  which  ir- 
sounds  to  the  fork's  fundamental  tone.  An  almost  pure  simple 
sound  can  be  obtained  by  softly  blowing  a  closed  organ-pipe. 
On  examining  the  nature  of  the  vibratory  motions  of  the 
prongs  of  the  fork:^  and  of  the  molecules  of  air  in  the  resound- 

*  This  paper  it  the  fifth  in  the  series  of  those  on  Aeoustict  aliesdy 
published  m  the  Philosophical  Magaxine.  The  preceding  papers,  however* 
were  not  numbered. 

t  Communicated  by  the  Author,  with  corrections,  from  Silliman*s  Ame- 
rican Journal  for  August  1874. 

Sections  1,  2,  3,  b,  6,  and  7  of  this  paper  were  read  before  the  National 
Academy  of  Sciences  during  the  Session  of  Norember  1873.  Section  4  was 
read  before  the  Academy  on  April  21,  1874. 

X  In  my  course  of  lectures  on  Acoustics,  I  thus  show  to  my  students 
that  the  prong  of  a  tuning-fork  vibrates  like  a  pendulum : — I  take  two  of 
Lissajous's  reflecting  forks,  giving,  say,  the  major  third  interval,  and  with 
them  I  obtain  on  a  screen  the  curve  of  this  interval  in  electric  light.  On 
a  glass  plate  I  have  photographed  the  above  curve  of  the  major  Uiird  pas- 
sing through  a  set  of  rectangular  coordinates  formed  of  the  sines  of  two  cir- 
cles whose  circumferences  are  respectively  divided  into  20  and  25  equal 
parts.  I  now  place  this  plate  over  the  condensing-lens  of  a  vertical  lantern 
and  obtain  on  the  screen  the  curve,  the  circles,  and  their  net  of  coordinates. 
Suspended  over  the  lantern  is  a  Blackburn's  compound  pendulum*  which  is 
so  constructed  that  its^'  bob  "  cannot  rotate  around  its  axis.  The  bob  is 
hollow,  and  a  curved  pipe  leads  from  its  bottom  to  one  side  of  the  pendulum. 
The  pendulum  is  now  defiected  into  a  plane  at  45*^  with  its  two  rectangu- 
lar planes  of  vibration,  so  that  the  end  of  the  curved  pipe  coincides  with  the 
beginninff  of  the  curve  over  the  lantern.  The  bob  of  the  pendulum  is  fas- 
tened witn  a  fine  cord  in  this  position,  and  fine  hour-glass  sand  is  poured 
into  it  j  the  cord  is  now  burned,  and  the  sand  is  delivered  from  the  pipe 
as  the  swinging  pendulum  gives  the  resultant  of  its  motions  in  the  two 
planes  of  vibratioB,  while  the  photograph^  ^rve  o^tbe.  lantern  is  pro- 


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Fh>f.  A.  M*  Mayer's  Eeitatehei  m  Acauftia.        267 

ing  eavity*  and  in  the  cloeed  organ-pipe f,  we  find  that  each  of 
these  vibrations  follows  the  same  law  of  reciprocating  motion 
as  governs  the  vibrations  of  a  freely  swinging  pendulum.  But 
other  bodies,  for  instance  the  free  reeds  of  organ-pipes  and  of 
melodeonsj^  vibrate  like  the  pendulum ;  yet  we  can  decompose 
the  vibrations  they  produce  in  the  air  into  many  separate  pen* 
dulum-vibrations^  each  of  which  produces  in  the  air  a  simple 
sound  of  a  definite  pitch*  Thus  we  see  that  a  pendulum-vi- 
brating body^  when  placed  in  certain  relations  to  the  air  on 
which  it  acts,  may  give  rise  to  highly  composite  sounds.  It  is 
therefore  evident  that  we  cannot  always  decide  as  to  the  simple 
or  composite  character  of  a  vibration  reaching  the  ear  solely 
from  the  determination  of  the  motion  of  the  body  originating 
the  sound,  but  we  are  obliged  to  investigate  the  character  of  the 
molecular  motions  of  the  air  near  the  ear,  or  of  the  motion  of  a 
point  on  the  drum  of  the  ear  itself,  in  order  to  draw  conclusions 
as  to  the  simple  or  composite  character  of  the  sensation  which 
may  be  produced  by  any  given  vibratory  motion.  Although  we 
cannot  often  detect  in  the  ascertained  form  of  an  aerial  vibration 
all  the  elementary  pendulum-vibrations,  and  thus  predetermine 
the  composite  sensation  connected  with  it,  yet  if  we  find  that 
the  aerial  vibration  is  that  of  a  simple  pendulum,  we  may 
surely  decide  that  we  shall  receive  from  it  only  the  sensation 
of  a  simple  sound.  Thus,  if  we  arm  the  prong  of  a  tuning- 
fork  with  a  point,  and  draw  this  point  on  a  btmp-blackened 
surface  with  a  uniform  motion  and  in  a  direction  parallel  to 
the  axis  of  the  fork,  we  shall  obtain  on  the  surface  a  sinusoidal 
or  harmonic  curve  §;  and  this  curve  can  only  be  produced 
by  the  prongs  of  the  fork  vibrating  with  the  same  kind  of 

gressively  covered  with  the  gand  if  the  times  of  the  two  vibrations  of  the 
pendulam  are  to  each  other  as  4  to  5. 

*  Helmholtz,  Tbnen^findmngen,  1857>  p.  75.  Grelle's  J<mm,fUr  Math., 
ToL  Ivii. 

t  See  Mach's  Optisch-ahutische  Versuche,  Prag,  1873,  p.  91.  Dig 
Stroboskopische  Darstellung  der  Luftschvoingvngen. 

X  The  Rey.  S.  B.  Dod,  one  of  the  trustees  of  the  Stevens  Institute,  has 
recently  made  an  experiment  which  neatly  shows  this : — He  silvered  the 
tips  of  two  melodeon-reeds,  and  then  vibrated  them  in  planes  at  right  angles 
to  each  other,  while  a  beam  of  light  was  reflected  from  them.  The  rdbul- 
tant  figure  of  their  vibrations  is  the  same  as  that  obtained  by  two  Lissajous's 
forks  placed  in  the  same  circumstances  and  having  the  same  musical  inter- 
val between  them  as  that  existing  between  the  reeds. 

§  The  equation  of  this  curve  is  y = a  sin  (^r^+  «  )  •   The  length,  on  the 

axis,  of  one  recurring  period  of  the  curve  is  X ;  the  constant  a  is  the  maxi- 
mum ordinate  or  amplitude.  The  form  of  the  curve  is  not  affected  by  a ; 
but  any  change  in  its  value  slides  the  whole  curve  along  the  axis  of  x.  It 
is  interesting  to  observe  that  this  curve  expresses  the  annual  variation  of 
temperature  in  the  temperate  zones. 


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268         Prof.  A.  M.  Meyer^s  Researches  in  Aeouatiesr 

motion  as  that  of  a  freely  swinging  pendnlum.  If  we  now  brin^ 
this  vibrating  fork  near  the  mouth  of  a  glass  vessel  whose  mass 
of  air  responds  to  the  tone  of  the  fork,  and,  by  the  method  of 
Mach,  examine  the  vibratory  motions  of  the  air,  we  shall  see  it 
swinging  backward  and  forward;  and  by  combining  these  vibra* 
tions  with  the  rectangular  vibrations  of  forks  placed  outside  of 
the  vessel  we  shall  obtain  the  curves  of  Lissajous*  If  the  mem- 
brane of  the  drum  of  the  ear  be  placed  in  connexion  with  the 
resounding  cavity,  it  must  necessarily  partake  of  the  motion  of 
the  air  which  touches  it,  and  ultimately  the  auditory  nerve  fibrilbe 
are  shaken  in  the  same  manner,  and  we  receive  the  sensation* 
of  a  simple  sound.  Here  the  mind  naturally  inquires  the  reason 
of  this  connexion  existing  between  the  sensation  of  a  simple 
sound  and  the  pendulum-vibration.  It  has  always  appeared  to 
me  that  the  explanation  of  this  invariable  connexion  is  that  the 
pendulum-vibration  is  the  simplest  vibratory  motion  that  the 
molecules  of  elastic  matter  can  partake  of,  and  that  the  con- 
nexion of  the  sensation  with  the  mode  of  vibration  is  the  con- 
nexion between  the  simplest  sensation  perceived  through  the 
intervention  of  the  trembUug  nerves,  and  the  simplest  vibration 
which  they  can  experience.  Indeed  the  pendulum-vibration  is 
the  only  one  which  produces  the  sensation  of  sound ;  for  if  any 
other  recurring  vibration  enters  the  ear,  it  is  decomposed  by  the 
ear  into  its  elementary  pendulum- vibrations ;  and  if  it  cannot 
be  so  decomposed,  then  the  given  vibration  is  not  recurring  and 
does  not  produce  in  us  the  sensation  of  sound,  but  causes  that 
which  we  denominate  noise.  This  remarkable  connexion  be- 
tween a  simple  sound  and  the  pendulum  or  harmonic  vibra- 
tion, together  with  the  fact  of  the  power  of  the  ear  to  decompose 
the  motions  of  a  composite  sonorous  wave  into  its  vibratory 
elements,  was  thus  distinctly  enunciated  by  Ohm : — The  ear  has 
the  sensation  of  a  simple  sound  only  when  it  receives  a  pendulum- 
vibration  ;  and  it  decomposes  any  other  periodic  motion  of  the  air 
into  a  series  of  penduhtm-vibrations,  each  of  which  corresponds  to 
the  sensation  of  a  simple  sound. 

We  have  seen  that  the  harmonic  curve  is  the  curve  which 
corresponds  to  the  motion  which  causes  the  sensation  of  a  sim- 
ple sound ;  but  a  molecule  of  vibrating  air  or  a  point  on  the 
tympanic  membrane  may  be  actuated  by  vibratory  motions 
which,  when  projected  on  a  surface  moving  near  them,  will 
develop  curves  which  depart  greatly  from  the  simplicity  of  the 
harmonic,  or  curve  of  sines  f;   but  nevertheless  these  curves 

*  See  Helmholtz  on  the  distinction  between  a  sensation  and  a  perception* 
Tonempfindungeny  p.  101. 

t  In  section  6  of  this  paper  I  have  constructed  several  important  curves 
corresponding  to  composite  vibrations. 


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Prof.  A.  M.  Mayer's  Researches  in  Acoustics,        269 

will  always  be  periodic  if  the  sensation  corresponding  to  their 
generating  motions  is  that  of  sound.  Now  Fourier  has  shown^ 
and  states  in  his  theorenii  that  any  periodic  curve  can  always  be 
reproduced  by  compounding  harmonic  curves  (often  infinite  in 
number)  having  the  same  axis  as  the  given  curve  and  having  the 
lengths  of  their  recurring  periods  as  1^  ^,  i,  {,  ke,  of  the  given 
curve ;  and  the  only  limitation  to  its  irregularity  is  that  its  ordi- 
nates  must  be  finite^  and  that  the  projection  on  the  axis  of  a 
point  moving  in  the  curve  must  always  progress  in  the  same  di- 
rection. Fourier  demonstrates  that  the  given  curve  can  only 
be  reproduced  by  one  special  combination,  and  shows  that,  by 
means  of  definite  integrals,  one  can  assign  the  definite  sinusoids 
with  their  amplitudes  and  differences  of  phase.  Now  Helm- 
hoitz*  has  shown  that  di£ferences  of  phase  in  the  constituent 
elementary  sounds  do  not  alter  the  character  of  the  compo- 
site sound,  and,  therefore,  that  although  the  forms  of  the  curve 
corresponding  to  one  and  the  same  composite  sound  may  be 
infinite  in  variety  (by  reason  of  differences  in  phase  in  the  com- 
ponent curves),  yet  the  composite  sound  is  always  resolved 
into  the  same  elements.  This  experimental  result  of  Helmholtz 
also  conforms  to  the  theorem  of  Fourier  in  reference  to  the 
curves  projected  hj  such  motions ;  for  he  has  shown  that  only 
one  series  of  sinusoidal  resolution  is  possible. 

Fourier's  theorem  can  be  expressed  as  follows : — The  con- 
stants C,  G|,  Cqy  &c.,  and  ay,  a^,  &c.,  can  be  determined  so  that 
a  period  of  the  curve  can  be  defined  by  the  following  equation f : — 


y  =  C  +  C,sin(?^+«,)  +  C,sin(2?^+^,) 


+  ... 


But  Fourier's  theorem  is  the  statement  of  a  mathematical 
possibility;  and  it  does  not  necessarily  follow  that  it  can  be  im- 
mediately translated  into  the  language  of  dynamics  without 
experimental  confirmation  ;  for,  as  Helmholtz  remarks,  '^  That 
mode  of  decomposition  of  vibratory  forms,  such  as  the  theorem 
of  Fourier  describes  and  renders  possible,  is  it  only  a  mathe- 
matical fiction,  admirable  because  it  renders  computation  facile, 
but  not  corresponding  necessarily  to  any  thing  in  reality  ?  Why 
consider  the  pendulum-vibration  as  the  irreducible  element  of 
all  vibratory  motion  ?  We  can  imagine  a  whole  divided  in  a 
multitude  of  different  ways;  in  a  calculation  we  may  find  it  con- 
venient to  replace  the  number  12  by  8  +  4,  in  order  to  bring  8 

*  Tonenmfindungenj  p.  190  f/  seq. 

t  For  other  and  more  convenient  forms  of  expression  of  this  theorem, 
as  well  as  for  a  demonstration  of  it,  see  pp.  62  and  60  of  Donkin's  'Acous- 
tics'— the  most  admirable  work  ever  written  on  the  mathematical  theory  of 
sound* 


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270        Prof.  A.  M.  Mayer's  Ruemrches  m  Acauitics. 

into  view ;  but  it  doet  not  neoesMtrily  follow  that  12  should  al- 
ways and  necessarily  be  considered  as  the  sum  of  8+^  Ia 
other  cases  it  may  be  more  advantageous  to  consider  the  number 
as  the  sum  of  7+5. 

''  The  mathematical  possibility^  esUblished  by  Fourier,  of  de* 
composing  any  sonorous  motion  into  simple  vibrations,  cannot 
authorise  us  to  conclude  that  this  is  the  only  admissible  mode 
of  decomposition,  if  we  cannot  prore  that  it  has  a  signification 
essentially  real.  The  fact  that  the  ear  effects  that  decomposition, 
induces  one,  nevertheless,  to  believe  that  this  analysis  has  a 
signification,  independent  of  all  hypothesis,  in  the  exterior 
world.  This  opinion  is  also  confirmed  precisely  by  the  Aict 
stated  above,  that  this  mode  of  decomposition  is  more  advanta- 
geous  than  any  other  in  mathematical  researches ;  for  the  me- 
thods of  demonstration  which  comport  with  the  intimate  nature 
of  things  are  naturally  those  which  lead  to  theoretic  results  the 
most  convenient  and  the  most  clear.'^ 

The  theorem  of  Fourier,  translated  into  the  language  of  dy- 
namies,  would  read  as  follows : — *'  Every  periodic  tfihraiory  motion 
can  ahiHtt/s,  and  always  in  one  mannery  be  regarded  a$  the  turn  of 
a  certain  fmnber  ofpendulum-vibratione/^ 

Now  we  have  seen  that  any  periodic  vibratory  motion,  which 
has  the  proper  velocity,  will  cause  the  sensation  of  a  musical  note, 
and  that  a  pendulum-vibration  gives  the  'sensation  of  a  iimple 
souud'*^;  therefore,  if  Fourier's  theorem  is  applicable  to  the 
composition  and  decomposition  of  a  composite  sonorous  wave,  ii 
will  be  thus  related  to  the  phenomena  of  sound: — ^^ Every  w- 
bratory  motion  in  the  atutitory  canal,  corresponding  to  a  musical 
sound,  can  always,  and  always  in  one  manner,  be  considered  as 
the  sum  of  a  certain  number  of  pendulum-vibrations,  corresponSng 
to  the  elementary  sounds  of  the  piven  musical  note.** 

Heretofore  we  have  called  in  the  aid  of  the  sensations  (as* 
sumed  to  be  received  through  the  motions  of  the  covibrating 
parts  of  the  ear)  to  help  us  in  our  determination  of  the  simpk 
or  composite  character  of  a  given  vibratory  motion ;  but  Fou« 
rier^s  theorem  does  not  refer  to  the  subjective  effects  on  the 
organ  of  hearing,  the  dynamic  function  of  whose  parts  are  yet 

♦  Professor  DonkiD;  in  his  'Acoustics/  Oxford)  1870,  p.  11,  advises  tk« 
use  of  tone  to  designate  a  simple  sound,  and  the  word  note  to  distinguish 
a  composite  sound.  His  reasons  are  *^  that  tone  (Gr.  r6poi)  really  means 
tension,  and  the  efiect  of  tension  is  to  determine  the  pitch  of  the  sonad  of  s 
string;"  while  a  musical  note  is  generally  a  composite  sound.  Professor 
Donkin  further  states, "  Helmholtz  uses  the  words  Kkmg  and  Ton  to  signify 
compound  and  simple  musical  sounds.  We  have  followed  him  in  adoptmg 
the  latter  term ;  but  such  a  sound  as  that  of  the  human  voice  could  haidfy 
in  Enslish  be  called  a  olanjf,  without  doing  too  mudi  vi<;4ence  to  established 


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Prof.  A.  M.  Mayer's  Re$earehe$  in  Acausties.        271 

very  imperfectly  understood.  Ohm's  theorem,  on  the  other 
hand,  refers  entirely  to  these  sabjective  phenomena  of  the  ear's 
analysis  of  a  complex  sensation  into  its  simple  elements.  As 
Fourier's  theorem  refers  only  to  the  decomposition  of  a  com- 
posite recurring  vibration  intQ  its  elementary  pendulum-vibra- 
tions, it  has  nothing  to  do  with  the  physiological  fact  of  the  co- 
relation  of  the  pendulum-vibrations  and  the  simplest  auditory 
sensation;  though  this  well-ascertained  relation  gives  us  the 
privilege  of  using  this  sensation  as  an  indicator  of  the  existence 
of  an  aerial  pendulum-vibration.  Hence,  as  Fourier's  theorem 
IB  entirely  independent  of  our  sensations,  we  must  endeavour  to 
verify  it  directly  by  experiments,  which  must  perform  the  actual 
decomposition  of  the  composite  periodic  motion  of  a  point  into 
its  elementary  pendulum-vibrations.  But  many  difficulties  pre* 
sent  themselves  when  we  would  bring  to  the  test  of  experiment 
the  dynamic  signification  of  Fourier's  theorem.  For  example, 
the  composite  sound-vibration,  on  which  we  would  experiment, 
emanates  from  a  multitude  of  vibrating  points;  parts  of  the 
resultant  wave-surface  differ  in  their  amplitudes  of  vibration; 
while  points  equally  removed  from  one  and  the  same  point  of 
the  body  originating  the  vibrations,  may  differ  in  their  phases  of 
vibration;  so  that  when  such  a  wave  falls  upon  oovibrating 
bodies  which  present  any  surface,  the  effects  produced  are  the 
result  of  extremely  complex  motions.  The  mind  sees  at  once 
the  difference  between  this  complicated  coneeption  and  the  sim* 
pie  one  embodied  in  the  statements  of  the  dynamic  application 
of  Fourier's  theorem. 

As  the  mathematician  decomposes  seriatim  every  point  of  the 
recurring  curve  into  its  harmonic  elements,  so  the  physicist,  in 
eonfirming  the  dynamic  application  of  Fourier's  theorem,  should 
decompose  into  its  simple  pendulum-vibrations  the  composite 
vibratory  motion  which  such  a  curve  represents,  and  indeed  re* 
froduces  when  it  is  drawn  with  a  uniform  motion  under  a  slit  in 
a  diaphragm  which  exposes  to  view  only  a  point  of  the  curve  at 
once.  Therefore  only  one  vibrating  point  of  the  composite  so- 
norous wave  should  be  experimented  on;  and  the  composite  vi<^ 
bratory  motion  of  this  point  should  be  conveyed  along  lines  to 

Joints  of  elastic  bodies  which  can  only  partake  of  simple  pen* 
ulum-vibrations.  All  of  these  essential  conditions  I  have 
succeeded  in  securing  in  the  following  arrangement  of  ap- 
paratus. 

A  loose  inelastic  membrane  (thin  morocco  leather  does  well) 
was  moimted  in  a  frame  and  placed  near  a  reed-pipe ;  or,  as 
in  other  experiments,  the  membrane  was  placed  over  an  opening 
in  the  front  of  the  wooden  chamber  of  a  (ireni^'s  free-reed  pipe. 
The  ends  of  sev^  fine  fibre*  from  a  silk-worm^s  ooooou  were 


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272        Prof.  A.  M.  Mayer's  Researches  in  Aeaustics. 

brought  neatly  together  and  cemented  to  one  and  the  same  point 
of  the  membrane,  while  the  other  ends  of  these  fibres  were  at- 
tached to  tuning-forks  mounted  on  their  resonant  boxes,  as 
shown  in  fig.  1.    In  the  experiment  which  I  will  now  describe 

Fi«- 1. 


eight  forks  were  thus  connected  with  one  point  of  the  membrane. 
The  fundamental  tone  of  the  pipe  was  Ut,,  of  128  vibrations  per 
second ;  and  the  pipe  was  brought  into  accurate  unison  with  a 
fork  giving  this  sound 'l^.  The  forks  connected  with  the  mem- 
brane were  the  harmonic  series  of  Ut,,  Vt^,  Sol,,  Ut4,  Mi4,  Sol4y 
Bi",  Utg.  In  the  first  stage  of  the  experiment  we  will  suppose 
that  the  fibres  are  but  slightly  stretched ;  then,  on  sounding  the 
pipe,  all  the  fibres  at  once  break  up  into  exquisite  combinations 
of  ventral  segments.  If  the  sunshine  fall  upon  a  vibrating  fibre 
and  we  look  on  it  obliquely  in  the  direction  of  its  length,  we 
shall  see  ventral  segments  superimposed  on  ventral  segments  in 
beautiful  and  changing  combinations.  On  gradually  tightening 
the  fibres,  we  diminish  the  number  of  their  nodes ;  and  on  reach- 
ing a  certain  dgeree  of  tension  with  fibres  1  m.  long,  I  have  seen 
them  all  vibrating  with  single  ventral  segments.  On  increasing 
the  tension,  the  amplitudes  of  these  single  segments  gradually 
diminish  and  at  last  disappear  entirely,  so  far  as  the  unaided 
eye  caii  discern ;  and  then  we  have  reached  the  conditions  re- 
quired in  our  experimental  confirmation. 

The  point  of  the  membrane  to  which  the  fibres  are  attached 
is  actuated  by  a  motion  which  is  the  resultant  of  all  of  the 
elementary  pendulum-vibrations  existing  in  the  composite 
sonorous  wave ;  and  the  composite  vibrations  of  this  point  are 

*  Since  the  number  of  beats  per  second  ffiyen  by  any  harmonic  (of  a 
pipe  out  of  tune  with  its  harmonic  series  of  forks)  will  be  as  the  order  of 
the  harmonic,  it  is  better  to  tune  a  reed  to  unison  with  a  fork  giving  one  of 
its  higher  harmonics*    I  generally  used  the  Sol,  fork,  or  the  3rd  harmonic. 


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Prof.  A.  M.  Maycr*8  Researches  in  Acoustics.        273 

sent  through  each  of  the  fibres  to  its  respective  fork.  Thus 
each  fibre  transmits  to  its  fork  the  same  composite  vibratory 
motion^  while  each  fork  can  onl^  vibrate  so  as  to  give  the 
simple  pendulum-vibration  of  a  simple  sound ;  for  each  fibre  is 
attached  to  its  fork  at  a  point  which  lies  in  the  upper  node  of 
the  s^ments  into  which  the  fork  divides  when  it  gives  its 
higher  harmonic.  Now,  if  Fourier's  theorem  has  '^  an  existence 
essentially  real/^  any  fork  will  select  from  the  composite  vibra- 
tory moticm  which  is  transmitted  to  it  that  motion  which  it 
has  when  it  freely  vibrates;  but  if  its  proper  vibration  does  not 
exist  as  a  component  of  the  resultant  motion  of  the  membrane^ 
it  will  not  be  m  the  least  affected.  Now  this  is  exactly  what 
happens  in  our  experiment ;  for  when  the  pipe  is  in  tune  with 
the  harmonic  series  of  forks,  the  latter  sing  out  when  the  mem- 
brane is  vibrated ;  but  if  the  forks  be  even  slightly  thrown  out 
of  tune  with  the  membrane,  either  by  loading  them  or  by  alter- 
ing the  length  of  the  reed,  they  remain  silent  when  the  sounding- 
pipe  agitates  the  membrane  and  the  connecting  fibres'*^*  Thus 
have  I  shown  that  the  dynamic  application  of  Fourier's  theorem 
has  "  an  existence  essentially  real.'' 

It  is  indeed  very  interesting  and  instructive  thus  to  observe 
in  one  experiment  the  analysis  and  synthesis  of  a  composite 
sound.  On  sounding  the  reed  it  sets  in  vibration  all  the  forks 
of  the  harmonic  series  of  its  fundamental  note ;  and  after  the 
reed  has  ceased  to  sound,  the  forks  continue  to  vibrate,  and 
their  elementary  simple  sounds  blend  into  a  note  which  approxi- 
mately reproduces  the  tiuibre  of  the  reed-pipe.  If  we  could  by 
any  means  obtain  all  of  the  elementary  vibrations  and  have  them 
with  their  relative  intensities  correctly  preserved,  we  should  have 
an  echo  of  the  sound  of  the  reed  after  the  latter  had  ceased  to 
vibrate ;  but  the  impossibility  of  thus  obtaining  the  highest  com- 
ponents of  the  reed,  and  the  difficulty  of  reproducing  the  relative 
intensities  of  the  harmonics  in  the  covibrating  forks,  allow  us 
but  partially  to  accomplish  this  effect. 

2.  An  Experimental  Illustration  of  Helmholtz's  Hypothesis  of 

AuMtion. 

The  experiment  which  we  have  just  described  beautifully  illus- 
trates  the  hypothesis  of  audition  framed  by  Helmholtz  to  account 
for  this,  among  other  facts — ^that  the  ear  can  decompose  a 
composite  sound  into  its  sonorous  elements.  Helmholtz  founds 
his  hypothesis  on  the  supposition  that  the  rods  of  Corti,  in  the 
ductus  cochleaiis,  are  bodies  which  covibrate  to  simple  sounds-* 

*  See  section  5  of  this  paper  for  an  account  of  the  degree  of  precision 
of  this  method  of  sonorous  analysis. 
Pm,  Mag.  S.  4.  Vol.  48.  No.  318.  Oct.  1874.  T 


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974  Prof.  J.  J.  M&ller  on  m  Uedumatl  PrineipU 

■omewhit,  I  imigine,  ai  lodkd  strings^  of  graded  kngtlis  and 
diameters  would  aet  in  itmilar  drenmstanoes.  The  Tibrntiona 
of  the  eompoeite  wave  fall  upon  the  membrane  plaeed  near  the 
reed  at  they  fall  upon  the  membrane  of  the  tympanum ;  and 
these  vibrations  are  sent  through  the  stretched  fibres  (or  ddicate 
splints  of  rye-straw,  which  I  have  sometimes  used)  from  the 
membrane  to  the  tuned  forks,  as  they  are  sent  firom  the  mem- 
brana  tympani  through  the  ossicles  and  fluids  of  the  ear  to  the 
rods  of  Corti.  The  composite  vibration  is  decomposed  into  its 
vibratory  elements  by  the  covibration  of  those  forks  whose  vi* 
bratory  periods  exist  as  elements  of  the  composite  wave*moti<m  j 
so  the  composite  sound  is  decomposed  into  its  sonorous  elements 
by  the  oovibrations  of  the  rods  of  Corti,  which  are  tuned  to  the 
elementary  sounds  which  exist  in  the  composite  sonorous  vibra* 
tion«  The  analogy  can  be  carried  yet  further  by  placing  Uie 
forks  in  line  and  in  order  of  ascending  pitch,  and  attaching  to 
each  fork  a  sharply*pointed  steel  filament.  If  the  arm  be  now 
stretched  near  the  forks,  so  that  the  points  of  the  filaments  nearly 
toueh  it  at  pmnts  along  its  length,  then  any  fork  will  indicate 
its  covibration  by  the  fact  of  its  pricking  the  skin  of  the  anoi 
and  the  localiiation  of  this  pricking  will  tell  us  which  of  the 
series  of  forks  entered  into  vibration.  The  rods  of  Corti  shake 
the  nerve-filaments  attached  to  them,  and  thus  specialise  the  po* 
sition  in  the  musical  scale  <^  the  elements  of  a  composite  sono- 
rous vibration.  Thus  a  complete  analog  is  brought  into  view 
between  our  experiment  and  Helmholtrs  comprehensive  hypo* 
thesis  of  the  mode  of  audition. 

[To  be  continued.] 


XL.  On  a  Mechanical  Principle  retuUing  from  Hamilton's  Theory 
qf  Motion.  By  J.  J.  MCllxb,  Profeuor  at  the  Polytechnic 
in  ZUrichf. 

WHEN  a  system  of  material  points  moves  under  the  influ* 
ence  of  forces  proceeding  from  the  reciprocal  attraction 
and  repulsion  of  the  points,  all  the  integral  equations  of  the  mo* 
tion  can,  as  Hamilton  has  shown|,  bcrepresented  by  the  par- 
tial differential  quotients  of  a  function  of  the  coordinates  (the 
primary  function),  in  a  manner  similar  to  that  in  which,  accord- 
ing to  Lagrange,  its  differential  equations  can  be  represented  by 
aid  of  the  partial  differential  quotients  of  the  force-function. 
Therein  the  primary  function  satisfies  two  partial  differential 
equations ;  but  even  one  of  these  equations,  as  Jacobi  demon- 

♦  For  ditcnnions  of  the  vibretory  phenomena  of  loaded  strings,  sec  Don- 
kin't '  Acoustics,'  p.  139,  and  Ilelmholtz's  Tonempfindungen,  p,  267. 
t  Tnnslated  from  PoggendorflTs  Annalen,  vol.  clii.  pp.  10^-131. 
J  Phil.  Trans.  1834,  1835. 


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reiuUingjrom  Hamilton^B  Theory  of  Motion.  275 

fttrated^  is  sufficient  for  its  definition.  The  primary  function  is 
a  complete  solution  of  this  differential  equation ;  and  any  com- 
plete solution  of  the  latter^  analogously  differentiated  according 
to  the  constants^  gives  the  system  of  the  integral  equations. 
Hence,  in  the  Hamilton-Jacobi  method,  the  entire  problem  is 
concentrated  into  the  one  integration  of  the  partial  differential 
equation,  in  contrast  to  Lagrange's  way  of  proceeding,  in  which 
only  single  integrals  are  found  by  aid  of  the  known  principles* 
The  integration  of  the  partial  differential  equation  was  developed 
by  Jacobi't^  generally  both  in  the  way  already  pursued  by  La^ 
grange  and  Pfaff,  and  also  by  a  new  and  grand  method,  both  of 
which  methods  have  been  adopted  in  a  series  of  more  recent 
works. 

The  theory  above  mentioned  has  recently  undergone  expan- 
sbn  in  two  respects.  If  the  investigation  by  Hamilton  and 
Jacobi  referred  to  actual  space,  for  which  the  element  of  a  line 
proceeding  from  a  point  is  capable  of  being  represented  by  the 
iquare  root  of  the  sum  of  the  squares  of  differentials  of  the  ordi* 
nates  of  the  point,  Lipschitsf  formed  a  more  general  conception 
of  the  problem,  inasmuch  as  he  assumed  the  line-element  to  be 
equal  to  the  pi\k  root  of  any  real  positive  form,  of  the  /7th  degreCi 
of  the  differentials  of  any  coordinates  of  the  point  in  question. 
The  element  of  its  integral  corresponding  to  the  primary  func« 
tion  becomes  the  sum  of  any  form  of  the  pih,  degree  of  the  dif- 
ferential quotients,  taken  according  to  time,  of  the  variables  and 
any  force-function  depending  only  on  the  variables— this  sum 
multiplied  by  the  time-element ;  so  that  the  problem  of  mecha« 
nics  is  changed  into  a  perfectly  general  one  of  the  calculus  of 
variations.  If,  further,  Hamilton  assumed  a  force-function 
which  depended  only  on  the  coordinates  of  the  moved  point,  and 
if  Jacobi  extended  the  investigation  to  a  force-function  explicitly 
containing  the  time,  Schering  j:  conceived  the  problem  in  this 
direction  more  generally,  introducing  forces  dependent  not  only 
on  the  position  but  also  on  the  state  of  motion  of  the  masses. 
This  dependence  is  so  chosen  that,  tmderstauding  by  R  the  re^ 
suiting  force,  and  by  dr  the  virtual  displacement  of  the  mass* 
points,  SR£&*  becomes  the  difference  oetween  a  total  variation 
and  a  total  derived  according  to  time ;  and  this  generalization  ii 
at  the  same  time  accomplished  from  Lipschitz's  enlarged  point 
•  of  view.     In  it,  therefore,  motions  can  be  treated  which,  for  in* 

*  ''Vorletongen  iibeir  Dynamik:  Nora  methodus"  &c.,  Borcbsrdt's 
Journal,  60. 

t  "Untersuchung  eines  Problems  derVariationsrechnung,"  Borcbardt's 
Journal,  74. 

X  Hamilton- Jacobi'sche  Tbeorie  fiir  Krafte,  deren  Maass  von  der  Bewe- 
gungder  Korper  abhangt/'  Abhiindl.derGdtting.Oes.derJVissenschASlS. 

T2      . 


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276  Prof.  J.  J.  Mullet  on  a  Mechanical  Principle 

atance,  satisry  Weber*^  law,  or  motions  in  Ghiass'a  and  Riemaun's 
space  of  multiple  dimensions. 

The  slight  improvement  of  the  physical  side  of  Hamilton's 
method  stauds  far  from  the  high  degree  at  which  these  analytical 
investigations  have  arrived.  An  essential  peculiarity  of  it  con-^ 
sists  in  this — that  it  passes  from  a  given  motion  of  the  svstem 
of  points  to  another  in  a  similar  manner  to  that  in  which  La- 
grange's process  passes  from  one  configuration  of  the  points  to 
another.  The  primary  function,  a  definite  integral  which  is  ex- 
tended over  the  original  motion,  undergoes  an  alteration  by  the 
Variation  of  the  arbitrarv  constants  of  the  motion ;  and  this  va- 
riation, or  that  of  a  similar  integral  representing  the  expenditure 
of  the  force,  is  given  by  Hamilton's  symbolic  equations  of  mo- 
tion. Hence  Hamilton's  method  differs,  secondly,  from  La- 
grange's (in  which  the  force-function  changes  according  to  the 
elements  of  the  given  motion)  in  the  same  way  as  the  variation 
differs  from  the  differentiation  of  the  functions.  This  second 
aspect  of  it  could  not  but  lead  immediately  to  a  new  treatment 
of  the  perturbations,  which  has  by  Hamilton,  Jacobi,  and  Sdie- 
ring.been  developed  into  a  series  of  new  systems  of  pertnrbation- 
formule. .  Only  the  above-mentioned  application  of  the  variation 
of  the  motion,  which  is  in  principle  only  a  particular  way  of  re- 
presenting the  latter,  is  not  the  essential  of  the  new  view ;  that 
must  much  rather  be  sought  in  similar  principles  to  those  on 
which  the  ordinary  differential  equations  of  the  mechanical  pro- 
blem are  based.  It  is  true  that  one  signification  of  these  prin- 
ciples, the  representation  of  individual  integrals,  does  not  here 
iM>me  into  consideration  in  the  indicated  general  process  of  inte- 
gration ;  their  physical  meaning,  however  (independent  of  the 
other),  which  was  proved  most  evidently  in  the  proposition  of 
4he  vis  viva,  especially  with  the  generality  given  to  it  by  Helm- 
lioltz,  remains  here  also;  and  this  iustifies  an  examination  of  it. 

Such  an  examination  of  the  physical  aspect  of  Hamilton's 
method  is  attempted  in  the  sequel.  It  appeared  the  more  re- 
quired, as  the  endeavours  of  physicists  to  deduce  the  second 
proposition  of  the  mechanical  theory  of  heat  in  a  similar  manner 
as  the  first,  from  purely  mechanical  conceptions,  clearly  per- 
mitted the  supposition  of  a  new  mechanical  principle.  Bolts- 
mann'i',  Clausiusf,  and  LedieuJ  have  succeeded  in  obtaining 
from  Lagrange's  differential  equations  the  proposition  mentioned: 
it  did  not,  however,  like  the  first  proposition,  come  from  a  uni- 
versal principle ;  but,  on  the  contrarVi  those  investigations  led 
to  new  mechanical  propositions,  which  certainly  did  not  possess 

♦  Wiener  SUiunosberickte,  vol.  liii.;  Po^j.  Ann.  vol.cxliii.  p.  211. 
t  Pogg.  Ann.  vol.  cxlii.  p.  433.    Phil,  Mi^.  S.  4.  vol.  xlii.  p.  161, 
J  Comptes  Rendus,  1873, 1874, 


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resuliingfrom  Hamilton's  Theory  of  Motion.         277 

the  amplitude  of  the  principle  of  the  vis  viva.  An  attempt  by 
Szilv*  to  get  the  proposition  out  of  Hamilton's  treatment  of  thq 
subject  comes  nearer  to  the  above  notion ;  only,  not  to  mentiop 
that,  on  account  of  a  limitation  adhering  to  the  form  in  which  it 
has  hitherto  appeared,  it  could  not  lead  to  the  general  deduction 
required,  it  does  not  approach  more  closely  the  physical  side  of 
this  method. 

It  resulted  from  the  investigation  that  the  new  treatment 
satisfies  a  general  principle  similar  to  that  satisfied  by  Lagrange's; 
for  perfectly  coordinate  with  the  proposition  of  the  vis  viva  is 
the  following : — In  a  motion  whose  equations  of  condition  and 
force-function  do  not  explicitly  contain  the  time,  let  the  primarv 
function  and  expenditure  of  force  respectively  be  denoted  by  V 
and  W,  so  that 

-V=r(T-U)rf/,    W=r2Trf/, 
Jo  Jo 

understanding  by  T  the  vis  viva,  and  by  U  the  force-function ; 
and  let  it  be  assumed  that  V  may  be  represented  as  a  function 
of  the  initial  and  final  coordinates  and  the  time,  W  as  a  function 
of  the  initial  and  final  coordinates  and  the  energy ;  then  for 
every  change  of  motion  occurring  during  an  element  of  time  dt 
the  relation 


dt     ^l    ht    J-"" 


holds,  in  which  the  symbol  d  signifies  the  whole  of  the  alteration 
which  is  connected  with  change  of  motion,  while  d  denotes  all 
alterations  of  V-hW  not  produced  by  variations  of  the  coordi- 
nates. Therefore^  in  every  motion  whose  equations  of  condition 
and  force-function  do  not  explicitly  depend  on  /,  the  change  of 
the  primary  function  and  force-expenditure  produced  by  the 
variation  of  the  coordinates  alone  is  =0.  The  two  quantities  W 
and  y  are  here  capable  of  a  physical  interpretation  similar  to  that 
of  T  and  U.  The  former  has  already  been  designated  by  Ha- 
milton as  the  vis  viva  accumulated  in  the  motion ;  the  significa- 
tion of  the  latter  results  from  a  peculiarity  of  the  entire  Hamil- 
tonian  theory  of  motion :  namely,  while  la  micanique  analj/" 
iique  prefers  to  introduce  the  forces  into  the  equations  of  motion, 
Hamilton's  treatment  involves  the  introduction  of  the  momen- 
tary impulses — ^indeed,  so  that  the  place  of  the  forces  is  taken  by 
those  impulses  which  at  each  instant  are  capable  of  producing 
the  velocities  actually  present.  Now,  in  a  group  of  motions, 
these  impulses  can,  analogously  to  the  forces,  be  represented  as 
negative  pai*tial  differential  quotients  of  a  function  of  the  coor- 

*  ^ofg'  Ann,  vol.  cxlv.  p.  295;   vol.  cxlix.  p.  74.    Phil.  Mag.  S.  4. 
vol.  xliu.  p.  339 ;  vol.  xlvi.  p.  426. 


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278         Prof.  J.  J.  Muller  on  «  Meehankal  Prine^U 

dinates  j  and  this  function  is  nothing  else  but  the  above-defined 
primary  function  of  the  system.  This  peculiarity  gives  to  the 
primary  function  a  real  signification  simdar  to  that  obtained  by 
the  force-function  in  the  potential  energy,  and  makes  the  coor- 
dination between  the  principle  of  energy  and  the  new  proposi** 
tion  still  more  evident. 

If  this  proposition  was  the  general  principle  at  which  those 
investigations  of  the  theory  of  heat  aimed,  it  must  have  included 
as  a  special  case  the  second  proposition  of  that  doctrine,  in  the 
same  way  as  the  principle  of  energy  included  the  first  In  this 
relation  it  is  remarkable  that,  applied  to  the  mechanical  theory 
of  heat,  it  leads  direct  to  the  second  main  proposition  as  soon  as 
we  make  the  apparently  indispensable  supposition  that  the  tem« 
perature  of  bodies  is  proportional  to  the  vis  viva  of  their  mole- 
cular motion.  Corresponding  to  this,  the  principle  seems  also 
capable  of  a  series  of  further  applications  like  those  of  the  prin- 
ciple of  energy ;  those  which  will  be  here  given,  however,  are 
limited  to  the  case  belonging  to  the  theory  of  heat. 

The  proposition  cited  resulted  from  the  combination  of  two 
long-known  mechanical  equations.  Hamilton,  namely,  had 
given  his  equations  of  motion  both  in  reference  to  the  function 
y  and  in  reference  to  the  function  W ;  and  the  separate  results 
needed  only  to  be  combined,  in  order  at  once  to  furnish  the  new 
one.  It  would  be  obtained  in  the  most  general  form  by  intro- 
ducing the  integral  elements  generalized  in  the  sense  of  Lip- 
schits  and  Schering.  As,  however,  the  essential  point  was  its 
application  to  real  physical  motions,  and  it  had  to  be  presented 
first  in  its  simplest  form,  I  have  preferred  to  give  it  in  connexion 
with  the  older  method  of  Hamilton  and  Jacobi,  which  moves  en* 
tirely  on  this  ground.  But  then  this  process  must  in  another 
respect  be  conceived  more  generally ;  for,  in  every  form  in  whidi 
it  has  hitherto  been  carried  out,  it  presupposes  the  force-func- 
tion unaltered  in  form  with  the  variation  of  the  motion,  while 
such  an  alteration  of  form  is  sometimes  essential  in  physical 
considerations.  This  is  the  case,  for  instance,  with  the  mole- 
cular motions  designated  as  heat,  as  soon  as  the  bodies  are  sub- 
jected to  changes  of  volume  and  pressure.  In  regard  to  the 
quantities  accentuated  especially  by  Clausius,  which  occur  toge- 
ther with  the  coordinates  in  the  force-function,  and  vary  with 
the  variation  of  the  motion,  while  they  remain  constant  within  a 
given  motion,  it  was  therefore  needful  that  the  method  should 
be  amplified ;  and  this  has  led  to  a  somewhat  more  general  form 
of  the  equations  of  motion. 

§1. 

Given  a  system  of  n  material  points  reciprocally  attracting  and 


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ruuUingfrom  Hamilton's  Theory  of  Motion.  370 

repelling,  but  subject  to  no  other  forces,  so  that  the  soliciting 
forces  can  be  represented  by  the  negative  partial  differential 
quotients  of  a  fnnction  of  the  coordinates  of  all  the  points,  the 
force*function  U.  This  function  contains  as  variable  quantities 
at  all  events  the  coordinates  g^  of  the  points  in  motion,  of  which 
it  is  here  always  presupposed  that  thev  identically  satisfy  at  any 
moment  the  eouatious  of  condition,  of  whatever  form>  and  there- 
fore, if  m  sucn  equations  are  given,  occur  to  the  number  of 
8n-*mr;i/i.  Moreover  the  time  /  may  appear  explicitly  in  the 
force-function,  as  well  as  other  quantities  Ck,  which  change  only 
when  a  transition  takes  place  from  one  motion  to  another.  For 
motions  of  this  general  sort,  Hamilton's  method  for  gaining  the 
general  symbolical  equation  of  motion  which  refers  to  the  varia- 
tion of  the  motion  is  to  be  extended.  If  the  via  viva  of  the 
point-system  be  denoted  by  T,  and  the  primary  function  Y  Re- 
fined by 


-"-!>- 


V)dl, 


the  problem  is  nearer  to  that  of  finding  the  variation  of  this  inte- 
gral on  the  hypotheses  made. 

In  forming  this  variation,  the  time  /  is  fii'st  regarded  as  an 
independent  variable  which  is  not  variated.  All  the  quantities 
present  in  the  primaiv  function  are  therefore  regarded  as  func- 
tions of/  and  a  number  of  arbitrary  constants;  and  from  the 
variation  of  these  constants  alone  will  the  variation  of  those 
quantities,  and  hence  that  of  the  primary  function,  result.  Of 
such  arbitrary  quantities  there  will  always  be  2/jl  in  the  quantities 
mentioned,  which  can  be  supposed  to  arise  from  the  iutegration 
of  the  /A  differential  equations  of  the  second  order  of  the  motion ; 
but  since  a  variation  of  the  force-function  on  the  transition  from 
one  motion  to  another  is  presupposed,  to  those  2/i  constants  any 
number  of  others  may  be  added ;  these  latter,  which  at  all  events 
are  assumed  to  be  independent  of  one  another,  are  the  quantities 
c^  If,  then,  these  2/i+v  constants  change,  but  /  be  supposed 
unchanged,  we  obtain 

-8V=Sr(T-U)rf/«  rS(T-U)rf/, 
Jo  Jo 

and  we  have  only  to  do  with  the  variation  of  the  quantity  (T-*U). 
Since  the  equations  of  condition  of  the  system  may  explicitly 
contain  the  time  t,  the  vis  viva  T  will  in  general,  as  well  as  the 
force-function  U,  likewise  explicitly  contain  it;  but  since  the 
time  is  not  variated,  in  the  formation  of  the  total  variation  5V 


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280  Prof.  J.  J.  Muller  on  a  Mechanical  Principle 

there  occur  only  the  variations  8y,,  hq\,  hcj^  and  we  have 

By  partial  integration  in  the  second  part  of  the  right-hand 
side  there  hence  results,  if  the  values  of  the  various  quantities 
for  the  time  /=sO  be  denoted  by  the  index  0, 

and  if  we  put  the  dtiferential  quotients  of  the  via  viva,  taken  ac- 
cording to  y'p 

according  as  they  are  referred  to  the  time  /  or  to  the  initial  time 
0,  we  get 

This  is  an  equation  of  motion  of  the  most  general  kind,  similar 
to  one  to  which  prominence  is  given  b^  Jacobi*  and  to  another 
by  Scheringt ;  but  it  has  the  peculiarity  that  the  quantities  r^, 
not  contained  in  the  latter  equations,  occur  in  general  in  the 
force- function  likewise. 

AH  the  quantities  in  equation  (1)  are  presumed  to  be  functions 
of  /  and  2/i+v  arbitrary  constants,  of  which  the  first  2/i  have 
arisen  from  the  integration  of  the  differential  equations  of  the 
motion.  The  quantities  y^,  q\  can  now,  by  means  of  the  integral 
equations,  be  expressed  by  the  arbitrary  constants  and  /;  but 
by  the  same  integral  equations  the  2/i  arbitrary  constants  can 
also  be  represented  by  the  quantities  q^^  q^,  and  t.  Let  the  latter 
be  presupposed.  Then  Y  becomes  a  function  of  /  and  2/jl  quan- 
titics  q^,  q^ ;  but  it  contains  in  addition  the  arbitrary  constants  r^^ 

*  Vorhsungen  uber  Dynamik,  pp.  143,  356. 
t  HamiUon^Jaeobi'sche  Theorie,  p.  19. 


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resulting  from  Hamilton's  Theory  of  Motion^  281 

which,  in  consequence  of  the  supposition  made^  are  not  connected 
with  one  another  by  any  relation.  Hence  all  the  variations 
iq^,  iq\f  Bcj^  become  mutually  independent. 

In  consequence  of  this^  equation  (1)  can  be  immediately  split 
up  into  single  equations.  Puttings  that  is  to  say,  the  expression 
which  stands  under  the  integral-symbol 


^B-'-%=Ph"'- 


we  get  the  differential  equations  of  the  motion 

dt  ""        ^g,       ' 

and  as,  conversely,  the  latter  are  demonstrated  by  Lagrange  to 
be  independent  of  equation  (1),  it  follows  that  the  expression 
standing  on  the  right-hand  side  under  the  integral-symbol  va« 
nishes  under  all  circumstances.  Therefore  neglecting  it,  we 
have 


■8V=2i>^y,-2^:SgJ-£2|^M<J 


(2) 


and  this  is  Hamilton's  symbolic  equation  expanded.  Because, 
namely,  the  variations  are  all  independent  one  of  another,  they 
furnish  at  once  the  integral  equations 

Equation  (2),  with  only  an  unimportant  difference  in  the  way  of 
writing  it,  has  already  been  given  by  Clausius*;  it  is,  however, 
to  be  remarked  that  his  deduction  refers  only  to  motions  of  which 
the  force-functions  and  equations  of  condition  do  not  explicitly 
contain  the  time.  The  form  in  which  it  gives  the  variation  SV 
is  not  su£Sciently  general  for  the  following  considerations,  because 
in  general  the  time  t  likewise  varies,  and  therewith  a  partial 
change  is  produced  both  in  T  and  in  U  and  consequently  also  in 
V,  which  is  neglected  in  equation  (2). 

It  shall  therefore  now  be  assumed  that  the  time  t  is  no  longer 
the  independent  variable,  but  undergoes  the  change  Bt  on  the 
variation  of  the  motion.  In  order  to  understand  the  sense  of 
this  variation,  it  must  be  considered  that  the  time  is  not  to  be 
variated  wherever  it  occurs,  but  only  where  it  occurs  explicitly ; 
for  a  variation  of  the  other  would  amount  to  a  variation  of  the 
initial  and  final  coordinates ;  and  this  is  already  done.  In  this 
case,  therefore,  the  primary  function  V  is  taken  as  dependent  on 
the  initial  and  final  coordinates,  this  explicit  time  /,  and  the 
*  Pogg.  Ann,  vol.  cl.  p.  122. 


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383  Fiof.  J.  J*  MOUer  an  m  MmAaniMi  Prk^ctpk 

qumtitias  Cki  tnd  their  Tariatkm  it  to  be  ftmnedb^Tiriatingdl 
these  qoantities  timaltMieously.  Hence  the  total  variation  formed 
under  inclusion  of  the  time  becomes 

and  the  question  is^  to  determine  the  last  term  ^  • 

In  order  to  obtain  this^  let  it  be  remembered  that,  in  the  dif- 
ferentiation according  to  i,  the  quantities  e^  contained  in  the 
force-function  U  have  been  supposed  not  to  vary.  From  this  it 
follows  that 

and  from  thU  we  get  immediateljr  the  partial  differential  quotient 
•onght 

If  we  introduce  this  value  into  the  above  equation  for  8V,  the 
result  is 

-(U-T+2;>,9',)8/.    .    (3) 

This  general  equation  relative  to  the  variation  of  motion,  which 
corresponds  to  the  equations  7**^  aud  7a  given  by  Lipschitz, 
pp.  122,  138,  as  well  as  to  Schering's  equations  [5]  and  [6], 
p.  19,  oontaining  also  the  differential  equations,  is  also  valid,  as 
soon  as  a  force-function  exists,  when  the  force-function  and  equa- 
tions of  condition  explicitly  contain  the  time.  For  the  special  case 
which  alone  comes  into  consideration  in  the  following,  where  the 
time  does  not  explicitly  appear  in  the  force-function  and  condi- 
tions, it  takes  a  somewhat  simpler  form. 

That  is,  in  this  case  the  relation  holds, 

T+U=E, 
if  E  denotes  the  energy  of  the  system.     Hence,  if  we  add  and 
subtract,  on  the  right-hand  side  of  the  equation  for  ^,  the  value 
2T,  we  get 

|^=E  +  2;7,7,-2T. 

But,  with  the  hypotheses  laid  dowui  the  vis  viva  becomes  a  ho- 


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reiulttngjirmn  Uamilton't  Theory  of  Motion.  283 

mogemaoos  fanction  of  the  second  d^;Fee  of  the  variable  g'l ; 
therefore 

consequently  we  have  simply 

and  after  substitution  in  the  above  equation, 

-SV=Sp,Sy,-2pjSffJ-r2|^5c*rf/-E8<.    .    .     (4) 

This  form,  connecting  itself  with  Hamilton's  equation*^  is  the 
starting-point  for  the  following.  At  the  same  time  it  is  signifi*. 
cant  that  the  ordinary  equations  of  motion  of  Lagrange  are  re- 
garded as  satisfied  only  in  the  motion  itself,  and  not  during  the 
change  of  motion.  The  system  must  therefore,  in  the  motion, 
always  be  a  closed  one,  subject  to  no  action  from  without ;  on 
the  contrary,  during  the  variation  of  motion  such  an  action  from 
without  must  take  place.  Meanwhile  the  energy  of  the  system 
may  remain  constant  or  vary ;  whether  the  one  or  the  other,  has 
no  influence  on  the  validity  of  equation  (4).  This  independence 
of  Hamilton's  equation  upon  the  nature  of  the  variation  of  the 
motion  has  the  same  signification  as  that  of  Lagrange's  equation 
of  motion  upon  the  nature  of  the  variation  of  the  configuration » 
If,  therefore,  Lagrange's  method  reaches  to  systems  with  and 
without  conditions,  Hamilton's  equation  (4)  extends  to  systems 
which  with  the  alteration  of  their  motion  retain  the  energy  con- 
stant or  even  receive  energy  from  without. 

§2. 
Hamilton's  symbolic  equation  of  motion  plays  in  the  treat- 
ment of  the  mechanical  problem  a  part  like  that  of  the  symbolic 
equation  of  motion  of  Lagrange,  only  with  the  difference  that  it 
refers  to  the  variation  of  the  motion,  while  the  latter  concerns 
the  variation  of  the  configuration  in  a  motion.  If,  now,  in  La- 
grange's method  from  the  equation  of  motion  a  series  of  princi- 
ples result  which  have  partly  the  purely  analytical  signification 
of  integrals  of  the  differential  equations,  ana  partly  the  essen- 
tially physical  meaning  of  general  propositions  valid  for  motion 
generally,  the  question  arises  whether  similar  principles  do  not 
connect  themselves  with  Hamilton's  equation.  This  shall  be 
investigated  especially  in  regard  to  the  proposition  concerning 

•  Phil.  Tnuis.  1884,  p.  30/. 


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284  Prof.  J.  J,  Muller  on  a  Mechanical  Princgfle 

the  vii  viva,  which  has  acquired  by  far  the  greatest  importance 
in  Lagrange's  method. 

For  that  purpose,  the  already  indicated  presupposition  is  made, 
that  in  all  motions  henceforward  to  be  examined  time  does  not 
occur  explicitly,  either  in  the  force-function  or  in  the  equations 
of  condition ;  so  that  Hamilton's  equation  takes  the  form 

-SV=2;?,Sy,-2pJS}J-f  2|5^M^-E«/,    ...    (4) 
Jo      ^^k 

Making  use  of  the  well-known  substitution  given  by  Euler^  and 
employed  also  by  Hamilton  and  Jacobi^, 

V=-W-fE^, 
from  which 

SV=-8W+ES/  +  /8B, 

this  equation  of  motion  changes  into 


Herem 


SW^:Ep^q,-lp^hq^-C^^Scf^t  +  tSE (5) 

n 

W=-V+E/=r(T-U)rf/+(T+U)/=r(T-.U)rf/ 

Jt  Jo 

and  is  therefore  nothing  else  but  the  quantity  known  under  the 
name  of  the  expenditure  of  force.  It  is  to  be  understood  as  a 
function  of  the  quantities  q^,  q^,  E,  c^  ;  and  the  time  t,  which  in 
the  integral  in  equation  (5)  remained  over,  is  to  be  replaced  by 
the  equation 

so  that  /  and  E  in  equations  (4)  and  (5)  occupy  a  perfectly  ana- 
logous position,  in  such  sort  that  the  one  quantity  may  always 
replace  the  other.  If  now  the  two  relations  (4)  and  (5)  be  com* 
pared,  there  comes 

In  this  equation  the  variations  are  still  quite  undetermined. 
One  of  the  infinitely  many  systems  of  virtual  variations  will  now, 
under  the  suppositions  made,  be  the  system  of  the  variations 
which  enter  with  the  actual  change  of  motion  during  the  minute 
portion  of  time  dt.    Referred,  however,  to  these  actual  variationsi 

*  Compare  the  general  transformations  of  Lipscbitz  and  Schering. 


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resulting  from  Hamilton's  Theory  of  Motion.  285 

it  makes 

ind  the  second  and  third  terms  in  equation  (6)  can  each/ in  rela* 
tion  to  the  coordinates,  be  conceived  as  an  explicit  alteration 
according  to  /  which  may  be  expressed  by 


ilA 


Then  comes 

ffljm_[B<^]=„,  .  .  .  „ 

and  this  is  the  proposition  sought:  The  sum  of  the  alterations 
in  the  primary  function  and  the  force^ea^nditure,  which  are  pro* 
duced  by  the  variation  of  the  initial  and  final  coordinates  alone,  is, 
in  the  variation  of  every  motion  that  presupposes  a  force-function 
and  neither  contains  the  time  explicitly  in  this  nor  in  the  conditions, 
equal  to  nil. 

As  the  variation  of  the  motion  is  only  subject  to  the  condition 
that  it  does  not  destroy  the  limitations  of  the  system,  but  in  the 
rest,  as  already  shown,  may  very  well  take  place  under  accession 
of  energy,  the  proposition  we  have  gained  is  independent  of  the 
special  kind  of  the  accession.  In  this  relation  the  coordination 
with  the  proposition  of  the  vis  viva,  which  likewise  gives  the  in- 
crease of  the  latter  independent  of  the  kind  of  variation  of  the  con« 
figuration,  is  evident.  But  this  independence  forms  only  one  side 
in  the  latter  proposition ;  it  has  received,  as  is  known,  another, 
more  important,  through  the  remark  that  the  force-function  (in 
the  above  representation)  is  nothing  else  but  the  potential  energy 
of  the  system.  In  such  a  new  direction  the  new  proposition 
shall  now  be  investigated. 

The  sought  signification  of  the  primarv  function  readily  ap* 
pears  if  we  give  up  the  forces  on  which  the  ordinary  theory  of 
motion  rests,  and  introduce  in  their  place  momentary  impiuses 
capable  of  producing  the  velocity  existing  at  any  instant.  That 
such  a  manner  of  consideration  stands  in  essential  connexion 
with  Hamilton's  theory  of  motion  has  not  yet,  so  far  as  I  know, 
been  rendered  evident,  although  Thomson  and  Tait  have  recently* 
drawn  attention  to  the  importance  of  this  second  method  of  pro- 
cedure, not  inferior  to  the  first,  and  have  more  nearly  completed 
its  theory.  In  it  the  components  of  the  momentary  impulse 
(formed  according  to  the  general  coordinates),  if  the  components 
of  the  forces  taken  according  to  the  rectangular  coordinates  be 

♦  TreatiBe  on  Natural  Philosophy,  pp.  206  et  seqq. 


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686  Prof.  J.  J.  Miiller  on  a  Mechanical  Principle 

XYZ,  are 

On  the  other  hand,  if  tf  and  v  denote  the  componenta  (formed 
aeoording  to  the  coordinate  qt)  of  the  velocity  before  and  after 
the  impulse  Pf,  the  meohanioal  work  done  by  the  forces  during 
the  impulse  is 

L-P,^-. 

If  now  a  system  of  /i  impulse-components  Pj  be  presuppoaed^ 
which  shall  bring  forth  the  whole  of  the  velocities  ^t  from  the 
state  of  rest  of  the  system,  so  that  the  velocities  prec^ng  them 
are  all  kO,  but  the  velocities  after  them  those  70  then  the  me- 
chanical work  done  by  the  forces  during  the  impulse  becomes 

But  the  equivalent  vi$  viva 

therefore 

and 

-sl-'.^ <•' 

that  iS|  the  negative  partial  differential  quotients  of  the  primary 
function,  formed  according  to  the  coordinates,  represent  the 
components  of  the  momentary  impulse  which  is  capable  of  bring* 
ing  about  the  velocity  existing  at  the  time  in  question. 
If,  from  («),  the  vdue  of  P|  be  inserted  in 

af 
there  results  further 

and 

-x^dg,=2hdt} m 

that  is,  the  negative  partial  differential  of  the  primary  function, 
formed  according  to  the  whole  of  the  coordinates,  represents  the 

Sroduct  of  the  time- element  dt  into  twice  the  mechanical  work 
one  by  the  impulses  which  bring  forth  from  the  state  of  rest 
the  actual  velocities  q'i. 
If,  finally,  the  value  of  this  partial  differential,  from  (fi),  be 


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rmdiing  from  Hamilton's  Tkem)  of  Motion.  £87 

introdaoed  into  the  equation 


we  get 

and  from  this. 


V=J'(E-2L)rf/, (y) 

a  relation  which  is  immediately  obtained  from  the  earlier  defini* 
tion-eqoation  of  V  by  making  use  of  the  proposition  of  the 
energy,  was  used  by  Hamilton  without  hesitation  as  a  definition 
of  the  function  Y,  and  expresses  the  proper  mechanical  meaning 
of  the  primary  function. 

As,  then,  in  (7)  the  primary  function  appears  to  be  formed 
analogous  to  the  earlier  quantity  W,  it  will  be  convenient  to  in- 
dicate this  by  a  similar  notation ;  and  the  names  of  potential 
and  kinetic  action  may  commend  themselves  for  Y  and  W.  If 
we  put,  moreover, 

A«V+W=E/, 

and  name  this  simply  the  action  of  the  system,  equation  (7) 
changes  into 

#-[|^].o.  ......  <e, 

and  the  proposition  reads : — That  alteration  of  the  action  which 
is  conditioned  by  the  variation  of  the  initial' and  final  coordinata 
alone,  vanishes  with  the  change  of  every  motion  that  presupposes  a 
force-function  and  does  not  contain  the  time  escplicitly  either  in  this 
or  in  the  limitations.  In  this  form  it  may  be  designated  as  the 
principle  of  the  action. 

Here  {^ential  and  kinetic  action  are  quantities  characterizing 
the  given  motion  in  like  manner  as  the  potential  and  kinetic 
energy  the  corresponding  configuration*  If  we  imagine  the 
whole  series  of  constantly  altered  motions  to  be  run  through, 
they  will  in  general  be  distinguished  by  different  values  of  these 

Suantities :  in  proportion  as,  by  the  mere  alteration  of  the  coor* 
inates,  the  one  diminishes,  the  other  increases  through  the 
same  alteration;  so  that  in  this  new  view  perfect  correspondence 
exists  with  the  proposition  of  the  energy. 

In  regard  to  the  limitations  under  which  the  proposition  of 
the  action  has  been  obtained,  it  is  to  be  remarked  that  the  for- 
mation of  1  2Tdt,  like  that  of  T,  remains  possible  even  without 
a  force-function.    Now  the  question,  what  in  these  cases  becomes 


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288  Prof.  J.  J.  MuUer  on  a  Mechanical  Prineipk 

of  the  proposition  of  the  action  when  there  is  no  force-fanction, 
and  consequently  no  primary  function^  gives  occasion  to  bring 
oat  its  position  to  another  well-known  equation  in  medianicSy 
which  relates  to  the  above-mentioned  momentary  impulses. 

If,  namely,  the  components  of  the  impulses,  formed  according 
to  the  axes  of  the  rectangular  coordinates,  are  BHZ,  and  the  ve- 
locity-components  induced  by  them  are  s^y'sf,  the  equation  of 
motioA  i? 

2[{a-iiwp')&r+(H-my08y+ (Z-»»^S^]  =0. 

If  now  as  a  system  of  virtual  variations  the  actual  alterations  of 
the  coordinates  be  introduced,  there  results 

Integrated  over  the  given  motion,  there  comes 
Und  from  this  results,  by  variation. 


(9) 


This  is  the  equation  which,  in  the  general  case  assumed,  takes 
the  place  of  the  action-equation ;  its  terms  have  a  similar  mecha- 
liicu  meaning  to  that  of  the  terms  of  the  latter.  That  is  to  say, 
the  sum  of  the  left-hand  side  is  nothing  else  but  twice  the  me- 
chanical work  which  the  sum  of  the  forces  constituting  an  im- 
pulse perform  during  the  same.  The  equation,  therefore,  imme- 
diately passes  into 

'  'iTdt; (10) 


B('2Ldt=s(' 
Jo  Jo 


and  the  action-proposition  also  can  be  easily  brought  into  this 
form;  for,  according  to  (7), 


which,  inserted  in  its  equation,  furnishes  immediately  the  form 
(10) .  The  difference  between  the  two  cases  consists  only  in  this, 
that  in  the  case  of  a  force-function  the  terms  of  the  equation  are 
functions  of  the  coordinates,  in  the  other  case  they  are  not  so — 
relations  analogous  to  which  occur  likewise  with  the  proposition 
of  the  energy. 

§3. 

In  order  to  illustrate  the  principle  found,  which  represents  a 
characteristic  property  of  the  variations  of  motion  of  all  systems 
which  satisfy  the  oft-insisted-on  conditions,  a  simple  example, 


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resuliinfffrom  Hamilton's  Theory  of.  Motion.        .  289 

for  which  the  propoution  can  readily  be  verified,  may  first  be 
discussed.  For  tnis  I  select  the  motion  of  a  pendulum  which 
takes  place  in  the  vertical  plane  of  xy  about  the  downward- 
directed  axis  of  the  positive  y  in  infinitely  small  amplitudes;  and 
I  give  the  determination  of  the  two  functions  V  and  W  accord- 
ing to  known  methods''^. 

The  length  of  the  pendulum  being  denoted  by  /,  and  the  elon- 
gation each  time  by  9^  so  that 

x^lwOiOy    y^lcoH0, 

the  energy  E  expressed  by  the  quantities  Pi  and  q^  becomes 

B  =  i^-^/C08tf, 

where  ps^-».  Accordingly  the  differential  equations  of  the 
motion  are^  taking  account  of  the  infinitely  small  amplitude, 

d0_p 

and  the  two  integral  equations 

where  0q  and|>o  denote  the  values  of  0  and/?  for  /=0. 

Introducing  now  these  values  into  the  expression  for  the  vis 
viva 

and  substituting  for  the  squares  and  products  of  the  trigonome- 
trical functions  the  doubled  variables,  we  get 

-¥'\/?"°»\/?'- 

*  Compare  Hamilton's  and  Jacobi's  examples. 
PhiL  Mag.  S.  4.  Vol.  48.  No.  818.  Oct.  1874.  U 


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SgO         Prof.  J.  J.  Mailer  on  •  Mtiktamtl  Pvituirle 

When  theMunevilaesaK  alao  introdooed  into  the  fiHce-fiiactian 

there  remiUe,  aftar  a  eimikr  redoetioo, 

and  inserting,  finally,  both  these  values  m  the  primary  fonetion 

-V-fcT-U)*, 
we  obtain 

or^  if  by  aid  of  the  first  of  the  integral  equations  we  put 

and,  lastly,  introdnce  again  into  the  trigonometrical  fonctions  the 
simple  variables^ 

-\:r.gU  +  i{0'  +  0tily/7li>OtAyp—^Sllb^.       (11) 

Referred  to  the  same  variables  /  and  0,  we  have  on  the  othor 
hand 

If  this,  together  with  the  value  of  U,  be  inserted  in  the  known 
differential  equation  for  A, 

T«-U+E, 


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remUmg  from  Hantilton's  Theory  of  Motion,         291 
die  retttU  is 

and  from  tbu  the  integral 

W-JV2i^/»+2/«E-^/»fl«i^.    .    .      (12) 
If  we  now  form  out  of  (11)  and  (12)  the  differential  quotients 


Jt     nn^i; 


dW 
dd, 


=  -V'2^/»+2/«E-^/»^, 


and  introduce  them  into  the  action-equation,  we  get 


d8. 


-s/Zgl»-\-2m~gl»0l-^ 


'•         •  • 


(18) 

Indeed  it  ean  be  readily  shown  that  the  indiyidaal  derivata 
are  p  and  p^  respectively.  For  if  the  quantity  p^  be  eliminated 
from  the  second  of  the  integral  equations  for  example  by  aid  of 
the  first,  we  get  immediately 


tanA/^/       sin-v/l^ 


'^e 


and  if  we  put  this  value  of />  in  the  expression  of  the  energy,  it 
changes  into 


E= 


ir/«^cos«y^^^2y/WoC08^|/+^/^^ 


2/«sin 


and  hence 


\7f 


-'(-f)» 


aw 


/  gl'0*coH*^it-2gPB0oCOBAy' 
V  tin* A /it 


U2 


^jt+gl^e\ 


-=/». 


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29.2  Prof.  J.  J.  Miiller  on  a  Meehamcal  Principle 

Of  the  applications  of  the  proposition  of  the  action^  those  shall 
be  introduced  here  which  can  be  made  of  it  in  the  mechanical 
theory  of  heat.  If  heat  be  conceived  as  molecalar  motion,  the 
application  to  it  of  the  Ener^  proposition  leads  immediately  to 
the  first  main  proposition  of  this  doctrine.  Corresponding  to 
this,  we  are  now  mvestigating  what,  on  the  same  hypoth^ia, 
resalts  from  the  Action  theorem.  These  molecular  actions  are 
stationary  motions  of  a  system  of  points ;  and  the  simplest  case 
of  such  motions  is  obviously  that  in  which  all  the  points  move 
in  closed  paths,  and  with  a  period  common  to  all  of  them.  TUs 
shall  first  be  supposed. 

As,  for  closed  paths,  the  two  limits  of  the  integral  which 
forms  the  action  coincide,  when  the  integration  is  extended  over 
an  entire  revolution  we  obtain 


m  of  the  Action  propi 


and  hence  the  equation  of  the  Action  proposition  is  transformed 
into 


or,  written  explicitly, 

QCj^ 

If  now,  for  one  revolution,  we  name  the  mean  value  of  the  mt 
viva  T,  and  that  of  the  force-function  U,  we  obtain 


-y.j;(,-, 


-U)A=/(T-U), 

-<rsr=/iT-/iu+f*-tJ<ft, 

E=T+'U; 
and  if  we  insert  this  value  in  the  above  equation,  we  obtain 

from  which 

dU-.2|^&^=i?T+21Wlog/,      .    .    .    (14) 

a  well-known  equation,  already  advanced  by  Clausius'*'  for  audi 
motions. 

If  now  we  apply  this  or  related  equations  to  the  molecular 
♦  Pogg.  Ann.  vol.  cxUi.  p.  433.    Phil.  Mag.  S.  4.  vol.  xlii.  p.  161. 


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resulting  from  Uamiltoii^s  Theorjf  of  Motion.  293 

motion  designated  heat,  making  use  at  the  same  time  of  the  hy- 
pothesis that  the  temperature  is  proportional  to  the  vis  viva  of 
the  motion,  we  arrive  (as  Boltzmaun,  Clausius,  and  Ledieu  have 
shown)  easily  at  the  second  proposition  of  the  mechanical  theory 
of  heat.  In  general,  however,  the  motion  of  the  molecules  of  a 
body  does  not  take  place  in  closed  paths.  With  respect  to  fluids, 
for  example,  we  are  not  even  justiiSed  in  assuming  for  them  a 
fixed  mean  position ;  and  in  the  case  of  solids,  where  such  an 
assumption  is  indeed  necessary,  the  actual  motion  will  yet  be 
distributed  along  all  the  dimensions.  Now,  for  such  cases  Clau- 
sius  has  recently  called  attention  to  a  second,  analogous  equation, 
which  substitutes  another  hypothesis  for  that  of  closed  paths. 
A  more  direct  derivation  of  the  second  main  proposition  from 
the  theorem  of  the  action  shall  here  be  given. 

The  suppositions  which  have  been  made  respecting  the  system 
of  pNoints  representing  the  body  are  simply  that  the  motion  is  a 
stationary  one,  and  t^^t  it  is  infinitesimally  changed  by  the  com- 
munication of  an  elementary  quantity  of  heat.  The  subject  of 
investigation  is  the  quantity 

which  refers  to  the  variation  mentioned.  Since  infinitesimal 
alterations  of  the  velocities  in  the  time-particle  dt  produce  only 
infinitesimal  path-changes  of  the  second  order,  this  makes 

Further,  the  system  of  variations  -^  can  be  split  into  two. 

Let  the  first  be  the  distances  qidt  which  are  traversed  in  the  ori- 
ginal motion  during  the  time-element  dt  from  the  points  q^, 
Iliis  portion  furnishes  the  sum 

Let  the  second  partial  system  be  the  distances  Cidt  which  lead 
from  the  above-mentioned  last  positions  in  the  original  motion 
to  the  final  positions  in  the  changed  motion.  In  it,  under  the 
suppositions  made,  to  every  value  o{p  there  come  just  as  many 
positive  as  negative  e;  this  portion  therefore  furnishes  the  sum 

Accordingly,  for  the  infinitesimal  variation  which  in  the  sta- 
tionary motion  of  the  point-system  is  conditioned  by  an  infinitely 
small  quantity  of  heat. 


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294    APrimiipkrenMiiffJhmEmaSiUm'tTkimytfMttiom. 
Ilierefore,  introdaeiDg  th«  fanetion  "V, 

and  the  equation  of  the  aeiton  ean  be  written 


But  since 


we  have 


dVr^2tdf+2fdt, 


and  from  this 

rfE-2  |^ifc*=JWT+2'rrflog/, 
or 

^E-2||^,=2TJlog(/T) (15) 

Now  this  equation,  which  has  already  been  given  by  Siily* 
for  the  special  case  in  which  no  Ck  are  present,  the  paths  arc 
closed,  and  the  periods  are  the  same  for  all  the  points,  leads  im- 
mediately  to  the  second  proposition  of  the  mechanical  theory  of 
•?*Lr  •  .  ^  **^**  purpose  let  us  consider,  first,  that  the  left-hand 
side  of  It  IS  nothing  else  but  the  energy  which,  with  the  ehange  of 
the  molecular  motion,  is  communicated  to  the  body  as  heat  from 
without ;  and  therefore,  in  the  usual  noUtion  of  the  theory  of  heat, 

it  is  J  rfQ.    If  we  then  make  use  of  the  assumption  that  f  is 

proportional  to  the  absolute  temperature  8,  we  immediatel/ 

■8=^' (16) 

understanding  by  dS  a  complete  differential. 

Thus  the  Second  Proposition  is  derived,  like  the  First,  from 
a  general  mechanical  principle.  But  the  above  representatiofi 
permits  us  to  perceive  for  the  two  propositions  not  merely  this 

♦  Pogg.  Ann.  vol.  cxlv.  p.  295.    Phil.  Mag.  S.  4.  vpl.  xliii.  p.  339. 


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Mr.  J.  CVKuMtly  onMNewFommU  in  Definite  Int^als.    206 

confortnihr  of  position,  bat  d80  a  eommon  origin.  Tho  derelop- 
ment  of  the  variation  of  Hamilton's  integral  bias  the  peeoliarity 
that  it  leads  simultaneously  to  the  differential  and  integral  equa- 
tions of  mechanieal  problems.  This  remarkable  &ct  gives  to 
the  principles  of  Energy  and  Action  a  common  origin  in  the 
general  equation  of  motion ;  and  by  this  the  latter  b^mes  the 
connecting  band  foi^  the  two  propositions  of  the  mechanical 
theory  of  heat. 
Zurich,  April  1874. 

XLI.  On  «  New  Formula  in  Definite  Integrals. 

To  the  Editors  of  the  Philosophical  Magazine  and  Journal. 

11  Elysium  Row,  Calcutta, 
6BNTLBMBN3  Augurt  2, 1874. 

I  SEE  in  the  July  Number  of  your  Magazine  two  new  for- 
muln  in  definite  integrals  of  some  importance  are  given  by 
Mr.  Glaisher.  The  integrals  admit  of  a  direct  general  solution 
without  using  the  identity  on  the  right-hand  side  of  the  equa- 
tiouj 

^o-«i^+««^&c.  =  x^,  -  (r^t^- 

The  portion  to  the  left  is  evidently  equal  to 

1 


or  putting  Es=€^*, 
From  this 


I 


And  taking  the  limits  n  and  0^  the  value  for  this  particular  ease 
is 

E_i    IT  IT 

2  *  ^"*  2  '  ^''*' 
The  second  theorem  is  obtainable  in  the  same  way.    It  is 
udx 

i+^.(l+B««)'*^ 

=(1-E)-'.  {tan-'x-E*tan-'E**}<^,. 


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296  Mr.  F.  Guthrie  on  an  Absolute  Gatponometer. 

This  is  the  general  solation ;  and  where  the  limits  are  infinity 
and  cipher^  there  results 

(l-E)-'.J.{l-e-i}ao=|.{l+E»}-'*o. 

whieh  is  the  same  as  given  by  Mr.  Glaisher. 

It  is  evident  that  there  are  numerous  theorems  of  the  same 
kind,  such  as 

cos  Ej?  .  flo=flo~  1^  +  *^v 

sinEa?.flro=«i*.-  123**^-' 

which  will  give  definite  results  between  the  limits  infinity  and 
cipher. 

Yours  obediently. 

Jams  O^Kinealt,  B.CS. 


XLII.  On  an  Absolute  Galvanometer. 
By  Frederick  Guthrie  *. 

MESSRS.  ELLIOTT  have  constructed  for  me  a  galvano- 
meter which  willy  I  believe,  be  found  to  possess  for  some 
purposes  certain  advantages  over  those  at  present  in  use.     Its 

Erinciple  depends  upon  the  measurement  of  the  current-strength 
y  the  measurement  of  the  mechanical  force  necessary  to  bring 
toa  given  distance  of  one  another  two  electromagnets,  which 
are  excited  by  the  current  in  such  a  fashion  that  they  repel  one 
another. 

The  current'enters  at  a  by  the  screw-damp ;  thence  it  passes 
beneath  the  circular  wooden  stand  C  along  the  copper  wire  mb. 
It  rises  vertically  and  coils  round  a  soft  iron  mass/,  which  lies 
horizontal  and  tangential  to  the  axis  of  the  instrument.  It 
passes  down  And  across  the  centre  of  the  board,  then  rises  and 
coils  round  a  soft  iron  mass  /',  exactly  similar  and  similarly 
placed  to/,  but  on  the  opposite  side  of  the  instrument.  Having 
encircled/',  the  current- bearing  wire  again  descends,  and  carries 
a  mercury- cup  y,  through  whose  bottom  it  passes,  and  which  is 
exactly  in  the  axis  of  the  instrument.  The  current  then  leaves 
the  mercury  by  the  wire  t,  which  dips  into  it.  It  then  traverses 
the  wire  around  the  iron,  m.  Thence  it  crosses  the  instrument 
and  forms  a  spiral  around  m!,  after  which  it  passes  into  the  mer- 
cury-cup A,  and  so  to  the  binding-screw  c.   The  spirals  are  such 

*  Read  before  the  Physical  Society,  May  23^  1874.  Communicated  by 
the  Society. 


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Mr.  F.  Guthrie  em  mAb$obUe  Galvanometer.        297 

that  there  is  repulsion  between /and  m,  and  also  between  m!  and 
/'.    It  is  seen  that  the  magnetic  pair//'  is  fixed.      The  pair 


m  m!  is  movable  about  a  vertical  axis.  The  system  mm'  is  hung 
by  a  metal  or  glass  thread  k  from  the  rod  l,  which  works  stif9y 
through  the  nut  o.  The  latter  carries  an  arm  and  vernier,  p, 
which  slides  over  the  graduated  head,  q.    The  scale,  nut,  &c. 


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398  Ai9/jc«t  rup$eiins  New  Booh. 

are  tnpported  on  the  glass  tabe  r^  whieh  is  fastened  by  the  sap  t 
cm  to  the  plate-glass  disk  t,  which  rests  upon  the  tap  of  we 

!;las8  cylinder  u  clamped  upon  the  wooden  base  e  resting  on 
evelling-screws.  In  the  side  of  v  is  a  plate-glass  window,  w^ 
through  which  a  vertical  line  of  light  may  be  focused  upon  x  (a 
mirror  fastened  to  the  mrrl  system),  and  thence  thrown  upon  a 
scale  in  the  manner  which  is  now  so  often  employed. 

A  word  or  two  about  the  way  in  which  the  instrument  is  used. 
The  upper  plate  /  and  the  system  m  mf  are  removed  by  lifting  r. 
The  edge  of  u  is  rubbed  with  beeswax  to  prevent  t  from  slipping 
upon  it.  The  copper  wires  penetrating  the  cups  are  amalgamated 
and  a  little  mercury  poured  in.  Amalgamated  thin  platinum- 
foil  is  then  pressed  into  the  cups,  and  mercury  is  poured  upon 
this.  By  this  means  a  concave  meniscus  is  obtamed.  The  upper 
partis  then  replaced,  and  so  adjusted  by  turning  the  plate  /  and 
the  cylinder  u  that  the  mirror  x  is  parallel  to  the  window  v, 
when  the  axis  of  m  ni  makes  an  angle  of  about  15^  with  that 
oiff.  The  rod  /  is  adjusted  so  that  the  wires  of  m  mf  just  touch 
the  mercury ;  and  by  the  leveUing-screws  A  is  so  swung  that  m 
and^  and  ako  ni  and/',  are  exactly  opposite  to  one  another  and 
the  wires  in  the  centres  of  the  mercury-cups.  A  slit  of  light  is 
then  sent  through  w,  reflected  on  to  a  screen,  and  the  head  o  is 
then  turned  till  the  slit  is  split  bv  an  arbitrary  vertical  line  on 
the  screen.  The  reading  of />  is  then  noted.  A  current  passing 
through  the  system  forces  mwl  away  from//'.  Turn  the  head 
0  untu  the  slit  of  light  is  again  brought  to  the  mark  on  the  screen. 
The  angle  through  which  it  must  be  turned  is  directly  propor- 
tional to  the  magneto-repulsion — that  is,  to  the  square  of  the 
current-strength.  Many  of  the  laws  of  electrodynamics  may  be 
readily  illustrated  by  this  instrument;  and  not  only  may  differ- 
ent currents  be  compared  with  the  greatest  accuracy,  but  the 
absolute  mechanical  magneto-value  of  the  current  may  be  at 
once  arrived  at.  By  bringing  the  repellent  magnets  alwaj's  to 
the  same  distance  from  one  another,  a  whole  class  of  sources  of 
error  is  removed. 


XLIII.  Notices  respecting  New  Booh. 

First  Lessons  in  Theoretical  Mechanics.  By  (he  Eev.  Johh  F. 
Twisnm,  MJL,  Professor  of  Mathematics  in  the  Staff  CoUege, 
and  formerly  Scholar  of  Trtnity  College^  Cambridge,  London : 
Longmans,  Oreen  and  Co.    1874:  pp.  243. 

npHOSE  teachers  and  students  who  are  already  acquamted  wi^ 
-L  t^e  author's  large  Treatise  on  Medianics,  will  naturally  ex* 
peot  to^find  in  the  work  bow  before  us  perfect  exuct^ude  both  ia 


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Notices  rstpesting  New  Booh.  309 

and  esqpreseion;  nor  will  ther,  making  due  allowanoe 
for  the  cOflELculty  of  the  undertaking,  be  m  any  way  diflappointed. 
It  is^  not  an  easy  task  to  teaoh  eyen  the  first  principles  of  me- 
chanics to  those  of  whom  only  a  knowledge  of  jtnthmetic,  a  little 
Geometry,  a  few  rules  of  Mensuration,  an  aptitude  in  the  use  of 
compasses,  scale,  and  protractor,  and  enough  Algebra  to  solye  a 
simple  equatioa  are  demanded.  Tet  the  author  has  performed 
this  task  in  a  manner  which  shows  that  with  him  teaching  is  an 
art  of  which  he  is  an  accomplished  master.  It  is  true  tmkt  now 
and  then  he  is  obliged  to  omit  or  postpone  the  proofs  of  certain 
important  theorems  which  inyolye  a  knowledge  of  GFeometry  and 
Trigonometry  not  possessed  by  beginners.      In  the  parallelo- 

ri  of  forces  (art.  37),  for  instance,  the  student  is  told  to  find 
resultant  by  consianiction.  That  the  resultant  is  the  diagonal 
of  a  parallelogram  of  which  the  two  giyen  forces  are  adjacent  sides, 
is  assumed  to  be  true — ^the  reason  of  the  rule  being  giyen  in  a  sub- 
sequent cluster  (137),  to  which,  howeyer,  no  clue  is  ^yen.  And 
this  seems  a  suitable  place,  in  our  notice  of  Mr.  Twisden's  book, 
for  remarking  that  a  work  containing  so  much  matter  (&r  more 
than  at  first  sight  appears)  ought  cer^inly  to  be  furnished  with  a 
copious  index. 

That  the  centre  of  Rrayitjr  of  a  triangle  is  the  intersection  of  the 
three  straight  lines  which  join  the  yerfcices  to  the  middle  points 
of  the  opposite  sides,  is  a  proposition  also  giyen  without  proof 
(art.  18),  showinff  that  the  litue  Geometry  which  Mr.  Twisden 
requires  of  his  readers  does  not  eyen  extend  to  the  proof  of  so  simple 
a  theorem.  In  art.  18  (6)  we  are  told  that  <'  any  area  may  be 
conceiyed  to  be  made  up  of  a  number  of  parallel  straight  lines," 
a  conception  which  mujst  be  inconsistent  with  the  youmy;  geo- 
meter's notion  of  a  straight  line.  By  use  of  the  principle  of  limits 
in  finding  the  centre  of  grayity  of  the  surface  of  a  triangle,  this 
inconsistency  would  certamly  be  ayoided. 

The  book  consists  of  eight  chapters,  the  first  fiye  of  which  are 
made  as  simple  as  possible.  Each  chapter  is  followed  by  a  collec- 
tion of  excellent  questions,  not  less  than  foor  hundred  altbgether 
being  giyen  in  this  manner.  Besides,  nearly  two  hundred  complete 
solutions  of  useful  and  interesting  problems  are  scattered  through- 
out the  book,  inyaluable  to  those  who  study  without  a  teadier. 

There  are  also  Tables  of  Specific  Grayities,  Moduli  of  Elasticity, 
Tenacities,  and  Besistances  to  Compressions. 

We  rec(Hnmend  the  book  to  the  notice  of  that  numerous  class 
for  whom  it  is  speciaUy  intended — ^those  who  must  know  mechanics 
and  yet  possess  out  little  mathematical  knowledge — to  Students,  as 
beinff  suitable  to  the  curriculum  of  the  TJniyersity  of  London,  and 
to  all  Teachers,  on  account  of  the  always  clear,  ana  often  ingeniousi 
deyelopments  of  the  most  important  parte  of  the  subject. 


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800  Notice*  respecting  New  Booh. 

Supplement  to  the  First  Book  of  Euclid's  Elements,  eontaininff  ihe 
Sixth-Book  Propositions  proved  independently  of  the  Fifth  Book^ 
and  the  Elementary  Propositions  of  Modem  Geometry,  By  "Edward 
Botleb,  M.A.T.C.D.  Dublin :  Alejomder  Thorn.  1872  (12mo, 
pp.  60). 

Euclidian  Geometry.  By  Fbakcis  Cuthbebtsok,  MJL,  late  Fellow 
of  Corpus  C?iristi  CoUege,  Cambridge,  Head  Mathematical  Master 
of  the  City  of  London  School.  LondQa :  Mftcmillm  and  Co* 
1874  (fcap.  8yo,  pp.  266). 

The  titlepages  of  these  works  suffidentlj  indicate  their  pur- 
pose ;  they  are  intended  to  be  substitutes  for  Euclid's  G^eomet^T, 
or  for  nart  of  it,  and  while  retaining  the  form  and  spirit  of  the 
original,  to  improve  on  it  in  detail  and  to  supplement  its  supposed 
deficiencies.  Both  books  are,  to  all  appearance,  written  hj  madie- 
matidans  of  average  competency ;  and  one,  at  least,  of  the  authors 
(Mr.  Cuthbertson)  is  in  a  position  which  makes  it  highly  probable 
that  he  is  a  teacher  of  considerable  experience*.  But  though  this 
is  the  case,  we  regret  to  have  to  add  that,  after  having  looked  into 
these  books  with  some  care,  we  do  not  see  why  they  have  been  pub- 
lished. 

With  Mr.  Butler's  book  the  difficulty  is  not  so  great  as  with 
Mr.  Cuthbertson's.  We  may  surmise  that  it  is  adapted  to  s<Mne 
course  of  instruction  sanctioned  by  the  Commissioners  of  National 
Education  in  Ireland ;  and  if  so,  its  somewhat  fragmentary  form  is 
explained.  It  consists  of  a  number  of  propositions  designed  as  a 
substitute  for  Euclid*s  sixth  book,  and  a  selection  of  elementary 
propositions  on  Harmonic  and  Anharmonic  Section  and  some  allied 
subjects.  It  is  hardly  necessary  to  notice  this  book  further ;  and 
were  we  asked  for  the  reason,  we  should  regard  it  as  a  sufficient 
answer  to  state  that  Mr.  Butler's  definition  of  proportion  runs 
thus : — "  Four  straight  lines  are  said  to  be  proportionals,  that  is, 
the  same  ratio  the  first  to  the  second  as  the  third  to  the  fourth, 
when  the  rectangle  contained  by  the  first  and  fourth  is  equal  to 
the  rectangle  contained  by  the  second  and  third."  Putting  out  oi 
the  question  the  typographical  error  which  may  be  presumed  to 
exist  in  the  passage,  the  sentence  betrays  a  view  of  the  functi<m 
of  definition  which  is  above  or  below  criticism. 

Mr.  Cuthbertson's  book  covers  just  the  same  ground  as  Euclid*8 
Books  1-6,  and  the  first  twenty-one  propositions  of  Book  11.  He 
has  manifestly  expended  a  great  deal  of  care  and  thought  on  its 
composition,  and  yet  we  are  constrained  to  say  that  his  attempt 
to  improve  on  Euclid  is  a  failure.  In  the  first  place,  his  book  is 
about  as  Ions;  and  quite  as  abstruse  as  Euclid's.  In  the  next,  he 
has  increased  the  difficulty  of  his  task  by  adapting  his  book  to  a 
certain  form  of  examination  which  our  limits  will  not  allow  us  to 

*  We  do  not  know  what  position  Mr.  Butler  holds ;  he  calb  himself  *'  Pro- 
fessor Ao.  under  the  CommissionerB  of  National  Eduoation  in  IreUnd."  We 
are  wholly  in  the  dark  aa  to  the  meaning  of  the  *'  Ac." 


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Notices  rapecting  New  Booh.  801 

explain.  Then,  again,  the  substance  o£  his  book  seems  to  us  of  a 
far  inf eri(»r  qui^tj  to  Euclid's  :  this  is  no  more  than  might  be  ex- 
pected; but  we  will  giye  an  instance  of  what  we  mean.  Euclid's 
treatment  of  the  Corollaries  to  the  32nd  prop,  of  Book  1  is  not,  per- 
haps, wholly  proof  against  minute  criticism ;  still  i£  any  thing  be 
wanting  it  could  be  supplied  by  a  word  or  two  of  explanation ; 
and  surely  nothing  can  be  plainer  or  more  direct  than  his  method. 
Mr.  Cuthbertson,  however,  wishes  to  improye  upon  it,  and  he  does 
so  as  follows: — On  p.  39  he  gives  a  Corollary,  which  is  stated 
thus : — "  If  A  B,  B  C  are  two  straight  lines  respectiyely  parallel  to 
DE,  EF,then  shall  the  angle  ABCbe  equal  to  the  angleDEF." 
This  is  traie  or  not  according  to  the  direction  in  which  E  F  is  drawn : 
e.  g,  it  is  true  in  the  case  shown  in  Mr.  Cuthbertson's  diagram ; 
but  the  needful  qualification  is  not  given  in^the  Corollary,  nor,  so 
&r  as  we  have  noticed,  anywhere  else.  On  p.  48  this  Corollary  is 
used  to  prove  the  theorem  *'  if  the  sides  of  a  polygon  be  produced 
in  order,  the  exterior  angles  shall  together  be  equal  to  four  right 
angles."  The  proof  consists  in  taking  a  point  outride  the  polygon  and 
drawing  from  it  rays  parallel  to  sides  respectively.  This  proof,  of 
course,  may  be  made  perfectly  sound ;  but  in  the  case  before  us  it 
fails  owing  to  the  above-mentioned  ambiguity.  This  is  the  way  in 
which  he  treats  Euclid's  second  Corollary,  and  then  he  goes  on  to 
prove  Euclid's  first  Corollary.  The  method  is  in  no  respect  better 
than  Euclid,  and  the  way  of  stating  it  inferior  to  the  extent  of  in- 
accuracy. 

There  is  one  question  of  general  interest,  suggested  by  a  perusal 
of  Mr.  Cuthbertson's  book,  on  which  we  will  say  a  few  woi^s,  viz. 
"What  are  axioms?"  Td  the  mathematician  they  are  merely 
truths  of  geometry  assumed  without  proof,  as  premises  needful  for 
proving  other  truths  of  geometry.  It  is  usual  to  answer  that 
axioms  are  self-evident  truths.  But, not  to  say  that  the  question  at 
oAce  arises  "  Self-evident  to  whom  ?  "  it  is  to  be  observed  that  the 
question  "  How  do  we  come  by  our  knowledge  of  the  axioms  of 
geometry  ? "  is  one  with  which  the  mathematiGian,  as  such,  has 
nothing  to  do.  There  are,  of  course,  two  distinct  ways  of  answering 
this  question,  and  each  doubtless  capable  of  numerous  modifications. 
Some  hold  that  the  axioms  of  geometry  are  what  they  are  in  virtue 
of  the  conformation  of  the  mind  antecedently  to  all  experience  of 
space.  Others  hold  that  the  axioms  are  nothing  but  the  expression 
of  our  most  elementary  experiences  of  space,  and  that  what  is 
called  their  necessary  truth  is  merely  a  consequence  of  the  uni- 
formity of  our  experiences,  joined  to  the  absence  of  any  experience 
which  suggests  so  much  as  a  type  of  something  inconsistent  with 
them.  "We  believe  this  to  be  a  sufficiently  correct,  though  brief, 
stl^ment  of  the  two  rival  answers ;  and  the  observation  we  have 
to  make  on  them  is,  that  whether  either  or  neither  of  them  be  true 
is  a  question  wholly  outside  of  geometry. 

We  may  not,  perhaps,  be  justified  in  doing  more  than  suspecting 
(but  at  all  events  we  do  very  strongly  suspect)  that  the  reason  of 
Euclid's  12th  axiom  being  so  much  objected  to  is  that  many  mathe- 


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302  Noiicei  retp^iing  New  Booh. 

maticiaiiB  renrd  tha  former  m  ihe  correct  answer  to  the  abora 
question.  There  is  not  much  difficulty  in  bebeving  that  we  are 
bom  into  the  world  with  minds  so  constituted  that  as  soon  as  wo 
know  the  meaning  of  words  we  cannot  do  otherwise  than  hold  that 
things  equal  to  the  same  thing  are  equal  to  one  another;  hdt  na 
one  except  a  hardened  metaphysician  could  suiq[K)se  that  a  belief  of 
the  12th  axiom  is  produced  by  any  thin^  but  an  acgnaintmoe  witii 
the  actaal  properties  ot  space.  Accordmgly  many  wish  to  substir 
tute  for  it  something  which  is  more  "  self-eyident,"  «.  s.  something 
more  consonant  with  their  metaphysical  views. 

It  is  not  easy  to  see,  on  other  grounds,  what  adTantage  is  ffi*^ 
by  substituting;  <me  axiom  tor  another.  No  (me  has  any  dimcoli^ 
inunderstandmg  what  the  12th  axiom  means,  nor  in  seeing  that  it 
is  undoubtedly  true.  If  any  one  will  proye  the  conTerse  of  pro* 
position  27  without  assuming  more  than  the  first  eleyen  axioms 
and  the  first  27  propositions,  he  will  do  something  worthy  of  all 
honour.  But  when  the  question  is  to  proye  the  point  by  means  oi 
a  special  axiom  which  oi&rs  from  Sudid*s  our  interest  in  tha 
matter  is  but  small,  e.  g.  U  any  one  prefers  Playfair^s  azioBi  to 
Euclid's  we  do  not  know  why  he  should  not;  only  we  would  remaik 
that  it  is  merely  a  question  of  preference,  that  tiie  two  asdoms  an 
quite  coordinate  with  each  other,  and  that  if  either  is  taken  £or 
granted  the  other  can  be  immediately  proyed. 

Mr.  Cuthbertson,  however,  takes  a  oifEerent  view  from  this,  and 
he  goes  to  work  to  imnrove  upon  Euclid  as  follows  : — On  p.  83  ha 
gives  **  Deduction  G-,  vis,  "  If  points  be  taken  along  one  of  iho 
arms  of  an  angle  &rther  and  further  &om  the  vert^  their  dia» 
tances  [meaning,  as  explained,  perpendicular  distances]  from  the 
other  arm  will  at  length  be  greater  than  any  given  straight 
line.''  It  is  obvious  that  this  statement  as  it  stands  is  not  tme; 
however,  the  needful  correction  could  be  supplied  wiihont  mneh 
difficul^;  #•  g.  it  would  be  sufficient  for  present  purposes  fiir  it  to 
run,  '*  If  points  be  taken  at  equal  distances  ^^  and  this  is  wpfOr 
rently  what  is  meant.  Further,  the  demonstration  of  the  dedootoi 
assumes  that  any  angle  however  small  can  be  multiplied  until  an 
angle  is  obtained  greater  than  a  right  angle.  We  have  no  objeotioB 
to  t^  being  assumed,  onl^  to  its  being  assumed  implicitly.  In  a 
book  which  f  ormaUy  specifies  the  axioms  assumed,  it  ought  to 
have  been  separately  enunciated  as  an  axiom ;  and  we  canned  find 
that  this  has  been  done.  On  p.  34  Mr.  Cuthbertson  g^ves  the 
axiom  which  he  proposes  to  substitute  for  Eudid's  12th  axiom,  vis. 
"  If  one  straight  Ime  be  drawn  in  the  same  plane  as  another  it 
cannot  first  recede  from  and  then  approach  to  the  other,  neither 
can  it  first  approach  to  and  then  recede  from  the  other  on  Hie  sama 
side  of  it.*^  By  means  of  this  axiom  and  deduction  G,  he  succeeds 
in  proving  Playfair's  axiom.  In  other  words  (putting  accidental 
detects  out  of  the  question),  he  succeeds  in  proving  one  axiom  by 
assuming  two.  We  willingly  accord  to  this  the  praise  of  inpraiuity ; 
but  we  strongly  suspect  that  few  besides  the  author  will  thmk  it  an 
improvement  on  Euclid's  method. 


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Royal  Society.  808 

We  had  marked  for  notiee  our  author's  way  of  treating  the 
subject  of  proportion;  but  our  limits  will  not  allow  us  to  fulfil  our 
intention.  We  will  only  saj  that  it  seems  to  us  a  feasible  way  of 
treating  the  subject  (in  the  same  manner  as  his  treatment  of  paral- 
lels is  feasible^  but  as  to  its  being  an  improyement  on  Euclid's 
method,  that  is  quite  another  matter. 


XLIV.  Proceedings  of  Learned  Societies. 

KOTAL  80CIBTT. 

[Continiied  firom  p.  226.] 

Feb.  26, 1874.— Joseph  Dalton  Hoc^r,  C.B.,  President,  in  the 

Chair. 

'T^HB  following  communications  were  read : — 

-^     "Note  on  Displacement  of  the  Solar  Spectrum."    By  J.  H. 

N.  Hennessey,  rjt.A.S. 

The  following  experiments  were  made  with  the  (new)  spectro- 
scope (three  prisms)  of  the  Boysd  Society,  to  ascertain  for  uds  in- 
strument the  amount  of  displacement  in  the  solar  spectrum  from 
chanjB;e  of  temperature.  The  spectroscope  was  set  up  on  a  pillar 
withm  a  small  tent  at  a  time  ot  the  year  when  ike  thermal  range 
is  considerable :  the  cdlimator  was  placed  horizontal,  and  directed 
through  a  window  in  i^e  tent  to  a  heliostat,  which  was  made  to 
reflect  the  sun's  image  when  required.  On  closing  the  window 
darkness  preyailed  in  the  tent,  so  that  the  bright  sodium  linea 
were  easily  obtained  from  a  spirit-lamp.  Before  commencing,  the 
slit  was  adiusted  and  the  spectroscope  clamped ;  and  no  moy^nent 
of  any  kind  was  permitted  in  the  instrument  during  the  experi- 
ments. The  displacement  was  measured  by  means  of  a  micrometw 
in  the  eye-end  of  the  telescope,  readings  being  taken  (out  of  curio- 
sity)  successiyely  to  both  dark  and  bright  lines,  i. «.  to  K  1002*8= Dr 
and  K  1006*8 sDtr  A  yerifi^ed  thermometer  was  suspended  directly 
oyer  and  almost  touching  the  prisms.  The  meteorological  obser* 
yatory  referred  to  was  some  fiffy  yards  north  of  the  tent. 

Bejecting  obseryation  5  (in  the  following  Table)  because  the 
thermomet^  was  eyidently  in  adyance  of  the  prisms,  we  deduce 

By  Dsrk  lines,  displacement  equal    g 

Dr  to  Dt;  is  produced  by ... .  31*3  change  of  t^nperature. 
By  Bright  lines,  displacement  equal 

Dr  to  Dt;  is  produced  by. . . .  29*4  „ 

Mean....  30 

f  nnn  which  it  appears  that  the  displacement  in  question  may  not 
be  neglected  in  inyestigations  made  under  a  considerable  thermal 
range. 


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Mr.  J.H.N.  Hennessey  on  White  Lines  in  Solar  Spectrum.  805 

"  On  White  Lines  in  the  Solar  Spectrum."  By  J.  H.  N.  Hen- 
nessey, F.B.A.S. 

Extract  from  a  Letter  jrom  Mr,  Hennessey  to  Professor  Stokes. 

"  Mussoorie,  Not.  12, 187a 
*'  My  deab  Snt, — Aa  I  cannot  account  for  what  is  described  and 
drawn  in  enclosed,  I  hasten  to  place  the  same  before  you,  intending 
to  look  for  the  white  lines  in  question  so  soon  as  I  move  down  to 
a  lower  altitude.  Amongst  others,  no  doubt  KirchhofE  closely  ex- 
amined the  region  in  question,  without  notice  of  the  lines ;  and  this 
only  adds  to  my  perplexity,  unless  what  I  see  here  is  due  (1)  to 
altitude,  or  (2)  is  instrumental.  In  the  latter  case  I  cannot  ac- 
count for  the  absence  of  the  white  lines  at  Dehra,  where  I  ex- 
amined the  spectrum  generally  several  times ;  I  must,  however,  add 
that  without  close  examination  and  some  experience,  the  lines 
might  easily  be  passed  over.  But  if  instrument^,  to  what  are  they 
due  ?  I  very  much  regret  that  the  old  spectroscope  is  not  avail- 
able at  present  [it  had  been  temporarily  sent  elsewhere  for  a  special 

object]  to  enable  me  to  verify  the  phenomena " 

[In  the  drawing  sent  by  Mr.  Hennessey,  the  intervals  between 
the  dark  lines  are  coloured  green,  except  in  the  place  of  the  two 
white  lines.  To  transfer  this  distinction  to  a  woodcut,  an  additional 
horizontal  band  has  been  added  below,  in  which  only  those  parts 
of  the  drawing  which  are  left  white  appear  as  white,  while  in  the 
upper  part  the  white  of  the  woodcut  represents  the  white  or  green, 
as  the  case  may  be,  of  the  original. — G-.  G-.  S.]        -^ 

Part  of  Solar  Spectrum,  drawn  to  Kirchhoff*8  scaler  observed  at  MuS" 
sooric,  N.  W.  Provinces,  India,  Lat.  N.  30°  28',  Long.  E.  78°  4'  ; 
Height  6700  feet  above  sea  (about^,  toith  the  Spectroscope  belonging 
to  t^  Hoyal  Society. 


Note  for  diagram. — In  course  of  studying  the  solar  spectrum  for 
atmospheric  lines,  with  an  excellent  3-prism  (new)  spectroscope 
belonging  to  the  Eoyal  Society,  I  gradually  exteiided  my  searcn, 

PAi7.  Mag.  S.  4.  Vol.  48.  No.  818.  Oct.  1874.  X 

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806  RoifMlSomty;^ 

began  at  the  red  end,  until  on  arriyal  at  theiedonabontt  myatten- 
tionL  wm  atta^acted  by  ilie  faot  tliat  K  1657*1  Dy  no  meanB  appeared 
as  the  strong  line  depicted  in  Kirchhoffs  map,  Plate  EL  Cm  ex- 
amining tbis  xegian  oarefullj,  I  was  surprised  to  find  i^  oolimrless 
lines  shown  in  the  diagram ;  these  lines,  from  want  of  a  more  ap- 
propriate name,  I  shall  call  white  lines  (or  spaces);  they  cannot  ab- 
solutely be  described  as  bright  lines,  jet  they  doselr  resemble 
threads  of  white  floss  silk  held  in  the  light.  The  spec&oscope  in 
nse,  witJi  the  most  oonyenient  hi^est-power  eyepiece,  presents 
images  of  about  two  thirds  to  seyen  nintlis  of  those  drawn  in  the 
diagrami  the  former  are  exa^rated  by  reckoning  to  agree  with 
Kirchhoffs  millimetre  scale;  it  will  theiefore  be  readily  understood 
that  the  white  lines  do  not  present  striking  objects  in  the  spectro- 
scope, especially  about  the  time  of  sunset,  when  I  happened  first 
to  notice  them ;  the^  are  best  seen  about  noon,  when  their  resem- 
blance to  threads  of  white  floss  silk  is  very  close ;  but  once  sem, 
the  lines  in  question  can  always  bereadily  detected.  So  fiiras  imr 
instrumental  means  permit,  the  wider  line  extends  between  K 
1657*1  and  K  1658*3;  more  accurately  speaking,  it  fiJls  short  of 
the  latter  and  rather  underlies  the  former;  the  narrower  white  line 
is  underneath  K  1650*3,  sensibly  more  of  the  former  appearing 
beyond  the  edge  towards  yiolet  of  the  latter,  which  presents  the 
quaint  look  of  a  blade  Une  on  a  white  surface  enclosed  in  a  green 
band.  These  are  the  only  white  lines  in  the  speotirum  from  extreme 
red  to  F;  they  are  not  bright  (or  reyersed  Imes),  so  far  as  I  haye 
had  opportumty  to  judse.  Were  they  bri^t  lines,  the  question 
would  arise,  why  these  alone  should  be  reyersed  at  6700  feet  aboye 
sea.  like  the  black  lines  the  white  lines  grow  dim  and  disappear 
with  the  slit  opened  wide.  As  seen  here,  K  1657*1  is  senmbly 
weakw  than  K  1667'4,  whereas  KiiehhoS  assigns  5  5  to  the  former 
and  only  3  a  to  the  latter. 

March  12. — JoBeph  Dalton  Hooker,  C.B.,  President,  in  the  CSiair. 

The  following  communication  was  read  s — 

"  On  a  New  Deep-sea  Thermomet^."  By  Henry  Negretti  and 
Joseph  Warren  ISambra. 

The  Fellows  of  the  Boyal  Society  are  perfectly  aware  of  the 
assistance  afforded  by  Her  Majestys  Ooyemment  (at  the  request 
oi  the  Bojal  Society)  for  the  purpose  of  deep-sea  inyestigations, 
and  haye  been  made  acquainted  with  their  results  by  the  Aeports 
of  those  inyestigations  published  in  the  '  Proceedings  of  the  Koyal 
Society '  and  by  the  interesting  work  of  Professor  WyyiUe  Thom- 
son. Among  other  subieots,  mA  of  the  temperature  of  the  sea  at 
yarious  depths,  and  on  the  bottom  itself,  ig  dtike  greatest  import- 
ance. The  Fellows  are  also  aware  that  for  thb  purpose  a  peculiar 
thermometer  was  and  is  used,  haying  its  bulb  protected  by  an 
,  outer  bolb  or  casing,  in  order  that  its  indications  may  not  be  yiti- 
ated  by  the  pressure  of  the  water  at  yarious  depths,  that  piessure 
being  atx>ut  1  ton  per  square  inch  to  every  800  fiithoms.    This 


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Messrs.  Negretti  and  Zambra  on^^  De$j^$ea  Thermometer.    807 

tberounnetery  as  regards  the  protection  of  the  bulb  and  its  Hon- 
lial^ty  to  be  affecred  hj  pressure,  is  all  that  can  be  desired ;  but 
unf ortuiuktelj  the  onlj  thermometer  available  for  the  purpose  of 
registering  temperature  and  bringing  those  indications  to  the  sur- 
&ce  is  t^  which  is  oommonlj  Known  as  the  Six's  thermometer 
— an  instrument  acting  by  means  of  ^cohol  and  mercury,  and 
having  movable  indices  with  delicate  springs  of  human  hair  tied  to 
thekn»  This  form  of  instrument  registers  both  maximnm  and  mi» 
nimnm  temperatures ;  and  as  an  orfnary  out-door  thermometer  it 
is  verj  useful;  but  it  is  unsatisfactory  for  scientific  purposes^ 
and  for  tiie  object  for  which  it  is  now  used  (viss,  the  determination 
of  deep-sea  temperatures)  it  leaves  much  to  be  desired.  Thus 
the  alcohol  and  mercury  are  liable  to  get  mixed  in  travelling,  or 
even  by  merely  holding  the  instrument  in  a  horizontal  positiim ; 
.  the  inmces  also  are  liable  either  to  slip  if  too  &ee,  or  to  stick  if 
too  tight.  A  sudden  jerk  or  concussion  will  also  cause  the  in- 
strument to  give  erroneous  reading  bv  lowering  the  indices,  if 
the  bl«ir  be  downwards,  or  by  raismg  them,  if  toe  blow  be  uth 
wards.  Besides  these  drawbacks,  the  Six's  thermometer  causes  the 
observar  additional  anxiety  on  the  score  of  inaccuracy;  for,  although 
we  get  a  fnmimum  temperature,  we  are  bv  no  means  sure  of  the 
poiiS  where  this  minimum  lies.  Thus  nx)fessor  Wyville  Thomson 
says  ('Pepths  of  the  Sea,'  p.  139): — ^'^  The  de»^rmination  of  tern-* 
perature  has  hitherto  rested  chiefly  upon  the  reg^straoon  of  mini- 
mum tiiermometers,  It  is  obvious  that  the  temperature  registered 
by  mmimum  thermometers  sunk  to  the  bottom  of  the  sea,  even  if 
their  registration  were  unaffected  by  the  pressure,  would  only  give 
the  lowest  temperature  reached  Bcmewher^  between  top  and  bottom, 
not  neutiarihf  at  the  bottom  itself.  The  temperatures  at  various 
depths  might  indeed  (provided  they  nowhere  increased  on  goinf 
deeper)  be  determined  by  a  series  of  minimum  thermometers  placed 
at  mfferent  distances  luong  the  line^  though  this  would  involve 
considerable  difficulties.  Still,  tiie^  liability  of  the  index  to  slip, 
and  the  probability  that  the  indication  of  the  thermometers  would 
be  affected  by  the  great  pressure  to  which  they  were  exposed,  ren- 
dered it  very  desirable  to  control  their  indications  by  an  indepen- 
dent method."  Again,  at  page  299,  we  find : — "  I  ou^ht  to  men- 
tion that  in  taking  the  bottom  temperature  with  the  Six's  thermo- 
meter the  instrument  simply  indicates  the  lowest  temperature  to 
which  it  has  been  subjected;  so  that  if  the  bottom  water  were 
warmer  tlum  any  other  stratum  through  which  the  thermometer 
had  paased^  the  observations  would  be  erroneous."  Undoubtedly 
this  would  be  the  case  in  extreme  latitudes,  or  in  any  spot  where 
the  temperatiu*e  of  the  air  is  colder  than  that  of  the  ocean* 
Ge^rtainly  ttie  instrument  might  be  warmed  previous  to  lowering ; 
but  if  tbi  c^^t  water  should  bQ  on  the  sur&ce,  no  reading,  to  be 
depended  oppn,  could  be  obtained. 

It  wfl«  on  reading  these  passages  in  the  book  above  referred  to 
that  it  beaame  a  matter  (^  serious  consideration  with  us  wheth^  a 

xa 


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308 


Royal  Sociefy : — 


thermometer  could  be  constructed  which  could  not  possibly  be  put 
out  of  order  in  travelling  or  by  incautious  handling,  and  which 
should  be  above  suspicion  and  perfectly  trustworthy  in  ite  indica- 
tions. This  was  no  very  easy  task.  But  the 
instrument  now  submitted  to  the  Fellows  of  the 
Boyal  Society  seems  to  us  to  fulfil  the  above 
onerous  conditions,  being  constructed  on  a  plan 
different  from  that  of  any  other  self-register- 
ing thermometers,  and  containing  as  it  does 
nothing  but  mercury,  neither  alcohol,  air,  nor 
indices.  Its  construction  is  most  novel,  and 
may  be  said  to  overthrow  our  previous  ideas  of 
handling  delicate  instruments,  inasmuch  as  its 
indications  are  only  given  by  upsetting  the  in- 
strument. Having  said  this  much,  it  will  not 
be  very  difficult  to  guess  the  action  of  the  ther- 
mometer ;  for  it  is  by  upsetting  or  throwing  out 
the  mercury  from  the  indicating  column  into  a 
reservoir  at  a  particular  moment  and  in  a  par- 
ticular spot  that  we  obtain  a  correct  reading  of 
the  temperature  at  that  moment  and  in  that 
spot.  Ymt  of  all  it  must  be  observed  that  this 
instrument  has  a  protected  bulb,  in  order  to 
resist  pressure.  This  protected  bulb  is  on  the 
principle  devised  by  us  some  sixteen  years  since, 
when  we  supplied  a  considerable  number  of  ther- 
mometers thus  protected  to  the  Meteorological 
Department  of  the  Board  of  Trade ;  and  they 
are  described  by  the  late  Admiral  EitsBoy  in 
the  first  Number  of  the  *  Meteorological  Papers,* 
page  55,  published  July  5th,  1857.  Beferriiig 
to  the  erroneous  readings  of  all  thermometers, 
consequent  on  their  delicate  bulbs  being  com- 
pressed by  the  great  pressure  of  the  ocean,  he 
says: — "With  a  view  to  obviate  this  failing, 
Messrs.  Negretti  and  Zambra  undertook  to  make 
a  case  for  the  weak  bulbs,  which  should  trans- 
mit temperature,  but  resist  pressure.  Accord- 
ingly a  tube  of  thick  glass  is  sealed  outside  the 
delicate  bulb,  between  which  and  the  casing  is  a 
space  all  round,  which  is  nearly  filled  with  mer- 
cury. The  small  space  not  so  filled  is  a  vacuum, 
into  which  the  mercury  can  be  expanded,  or 
forced  by  heat  or  mechanical  compression,  with- 
out doing  injury  to  or  even  compressing  the 
inner  or  much  more  delicate  bulb:^ 

The  thermometers  now  in  use  in  the  *  Chal- 
lenger' Expedition  are  on  this  principle,  the  only 
difference  being  that  the  protecting  chamber  has 


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Messrs.  Negretti  andZamhrtk  on  a  Deqhsea  Thermometer.    809 

been  partly  filled  with  alcohol  instead  of  with  mercury ;  but  that 
has  nothing  to  do  with  the  principle  of  the  iavention. 

We  have  therefore  a  protected  bulb  thermometer,  like  a  siphon 
with  parallel  le^,  aU  in  one  piece,  and  haying  a  continuous  com- 
munication, as  in  the  annexed  figure.  The  s^e  of  this  thermo- 
meter is  pivoted  on  a  centre,  and,  being  attached  in  a  perpendi- 
cular position  to  a  simple  apparatus  (which  will  be  presenfly  de- 
scribed), is  lowered  to  any  depth  that  may  be  desu*ed.  In  its 
descent  the  thermometer  acts  as  an  ordinary  instrument,  the  mer^ 
cury  rising  or  &lling  according  to  the  temperature  of  the  stratum 
through  which  it  passes  ;  but  so  soon  as  the  descent  ceases,  and 
a  reverse  motion  is  given  to  the  line,  so  as  to  pull  the  thermometer 
to  the  B\irface,  the  instrument  turns  once  on  its  centre,  first  bulb 
uppermost,  and  afterwards  bulb  downwards.  This  causes  the 
mercury,  which  was  in  the  left-hand  column,  first  to  pass  into 
the  dilated  siphon  bend  at  the  top,  and  thence  into  the  nght-hand 
tube,  where  it  remains,  indicating  on  a  graduated  scale  the  exact 
temperature  at  the  time  it  was  tunied  over.  The  woodcut  shows  the 
position  of  the  mercury  after  the  instrument  has  been  thus  turned  on ' 
its  centre.  A  is  the  bulb ;  B  the  outer  coating  or  protecting  cy- 
linder ;  G  is  the  space  of  rarefied  air,  which  is  reduced  if  the  outer 
casing  be  compressed ;  D  is  a  small  glass  plug  on  the  principle  of 
our  Patent  Maximum  Thermometer,  which  cuts  off,  m  the  mo^ 
ment  of  turning,  the  mercury  in  the  column  from  that  of  the 
bulb  in  the  tube,  thereby  ensuring  that  none  but  the  mercury  in 
the  tube  can  be  transferred  into  the  indicating  column ;  E  is  an 
enlargement  made  in  the  bend  so  as  to  enable  the  mercury  to  pass 
quickly  from  one  tube  to  another  in  revolving ;  and  F  is  the  indi- 
cating tube,  or  thermometer  proper.  In  its  action,  as  soon  as 
the  thermometer  is  put  in  motion,  and  immediately  the  tube  has 
acquired  a  sb'ghtly  oolique  position,  the  mercury  breaks^off  at  the 
pomt  D,  runs  into  the  curved  and  enlarged  portion  E,  and  even- 
tually f  aUs  into  the  tube  F,  when  this  tube  resumes  its  original 
perpendicular  position. 

The  contrivance  for  turning  the  thermometer  over  may  be  de- 
scribed as  a  short  length  of  wood  or  metal  having  attached  to  it  a 
small  rudder  or  fan ;  this  fan  is  placed  on  a  pivot  in  connexion 
with  a  second,  and  on  this  second  pivot  is  fixed  the  thermometer. 
The  fan  or  rudder  points  upwards  in  its  descent  through  the  water, 
and  necessarily  reverses  its  position  in  ascending.  This  simple 
motion  or  half  turn  of  the  rudder  gives  a  whole  turn  to  the  ther- 
mometer, and  has  been  found  very  effective. 

Yarious  other  methods  may  be  used  for  turning  the  thermo- 
meter, such  as  a  simple  pulley  with  a  weight  which  might  be  released 
on  touching  the  bottom,  or  a  small  vertical  propeller  which  would 
revolve  in  passing  through  the  water. 


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810  a$ohgkal  BoeUty  :^ 

UOLMIOAI  SOOIKT* 

[Contiaued  from  p.  230  J 

Dooembmr  17tli,  ld73^~Pro£  BotuMiyi  F.BA,  T^oe-Preildetitj 
indieChair* 

The  fbllowing  commonioatioiui  were  read : — 

1.  **  Observationfl  on  some  features  in  the  Physical  QwAojtf  of  tho 
Outer  Himalayan  r^on  of  the  Upper  Punj&h,  India.''  By  A.  B. 
Wynne,  Esq.,  F.G.8. 

The  district  of  the  Upper  PunjAb  described  by  the  anther  con- 
sists of  crystalline,  granitoid,  syenitic,  and  schistose  rocks  far  in 
among  the  hills,  succeeded  by  slates  and  limestones,  possibly  of 
Silurian  age,  unconformably  overlain  by  Triassic  and  perhaps  older 
iDcks,  which  are  in  their  turn  unconformably  succeeded  by  a  series 
of  mutually  conformable  Jurassic,  cretaceous,  and  nummuutic  lime- 
stones and  shaly  beds.  These  secondary  and  Tertiary  beds,  which  are 
.  chiefly  limestones,  are  called  the  **  Hill  Limestones."  Beyond  these 
comes  a  zone  of  hiUs  and  broken  plains,  composed  of  sandstones,  clays, 
and  conglomerates,  of  great  thickness  and  of  Tertiary  age  (Eocene 
and  Miocene),  which  the  author  calls  the  ''  Murree  beds.*'  Thia  belt 
passes  generally  along  the  whole  southern  foot  of  the  Himalayas, 
from  Assam  to  AfghanisUin.  In  the  district  described  by  the 
author  it  is  bounded  on  the  south  by  the  Salt  Bange,  beyond  which 
stretch  tho  deserts  of  the  Punjftb  and  Sind. 

The  outer  Tertiary  belt  presents  a  gradation  towards  the  hill 
character.  Among  the  rocks  of  the  Murree  zone  there  are  harder 
beds  than  elsewhere;  limestones  occasionally  appear,  sometimes 
like  those  of  the  hiU-beds,  and  the  Hill  Nummulitic  limestones  may 
have  alternated  in  their  upper  part  with  the  Murree  beds.  The 
nummulitic  limestones  of  the  Salt  Bange,  containing  large  Bitalven 
and  Gasteropoda,  were  probably  of  shallow*water  origin,  whilst  the 
diminutire  organisms  of  the  Hill  Nummulitic  limestone  inhabited 
greater  depths. 

Contortion  of  the  strata  is  a  common  feature  of  the  country, 
affectmg  some  of  the  newest  Tertiary  beds  so  as  to  place  them  in  a 
vertical  position,  and  almost  everywhere  throwing  the  rocks  into 
folds,  producing  in  many  ca^es  invendons  of  the  strata. 

The  author  compares  these  rocks  with  those  of  the  Simla  area 
described  by  Mr.  Medlicott,  who  found  there  two  strong  imoon- 
formities,  namely,  between  his  Siwa^ik  and  Kalum,  and  Nalum  and 
Subathu  groups,  and  rejarded  the  whole  of  the  beds  of  the  outer 
Tertiary  detrital  2one  from  the  base  of  the  Subathu  group  upwards 
as  discordant  to  the  Himalayan  or'Hill-series  and  to  each  o^er. 

The  junction  of  the  newer  Tertiaries  with  the  rocks  forming  the 
higher  hills  of  the  outer  Himalaya,  both  In  the  Simla  area  and  in  the 
outer  Punj&b,  is  marked  by  disturbance,  distortion,  and  inversion  or 
abnormal  superposition  in  the  Tertiary  strata  along  the  contact. 


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Mode  of  Ocenmnoi  qfDianwndt  in  South  Africa*      811 

In  iha  Upper  Ftmjftb  the  jutustton  Mbws  a  curred  Hm^  raudng^ 
nenrhr  east  sad  wesi  to  the  nort^  of  Banml  Pindee ;  than  de« 
•erimiig  aa  an|^  whidi  doeelf  fottows  the  great  bend  of  the  Jhilam 
virer  near  Kocnfferabad,  it  rana  more  or  less  in  a  sontii-eaaterly 
direetkm  through  Kashmere  towards  Simla.  Thia  Jtmction  Ihie  is 
inaeparaldy  eonneeted  with  the  eauaation  of  the  great  mountain-' 
ehama ;  it  ahowa  a  panlleliam  to  the  axes  of  the  outer  ranges,  and 
is  Mety  due  to  intensity  of  disturbance^  the  result  of  bteral 
pressure* 

The  author  also  refers  to  the  difference  existing  between  the 
geology  ol  the  outer  Himalayan  region  and  that  of  &e  Salt  Bange, 
as  bong  similar  to  tiiat  wliioh  obtains  between  the  Alpine  and 
extra- Alpine  diaraeters  of  Eur(n>ean  nx^-groups,  and  suggests  that 
the  recurrence  of  such  similar  features  at  such  distances  may  indi- 
eate  a  connexion  between  the  former  eonditions  of  deposition  and 
the  early  history  of  the  great  chains  themselres. 

2.  ''  On  the  mode  of  occurrence  of  Diamonds  in  South  Africa.'^ 
By  E.  J.  Dunn^  Esq.  Communicated  by  Prof.  Bamsay,  FJEU3.« 
T.P.G.S. 

In  this  paper  the  author  stated  that  the  diamonds  of  South  AMca 
occur  in  peculiar  circular  areai^  which  he  regards  as  <*  pipes,''  which 
formerly  constituted  the  connexion  between  molten  matter  below 
and  surfece  Yolcanoes.  The  surrounding  country  counts  of  horizontal 
shales,  through  which  these  pipes  ascend  nearly  yertically,  bending 
upwards  the  edges  of  the  shales  at  the  contact.  The  rock  occupying 
uese  pipes  was  regarded  by  the  author  as  probably  Gabbro,  al« 
thon^  in  a  yery  altered  condition.  Intercalated  between  the  8hale« 
beds  there  are  sheets  of  dolerite  <&o. ;  and  dykes  of  the  same  rocks 
also  intersect  the  shales  at  firequent  intervals.  "Within  the  pipes 
tiiere  are  unaltered  nodules  of  the  same  dolerite.  With  regard  to 
the  relation  of  Ihe  diamonds  to  the  rock  of  the  ^ipes  in  which  they 
are  found,  tiie  author  stated  that  he  thought  it  probable  that  the 
latter  was  only  the  agent  in  bringing  them  to  the  surface,  a  large 
proportion  of  the  diamonds  found  consisting  of  fragments.  At 
the  same  time  he  remarked  that  each  pipe  furmshed  diamonds  of  a 
different  character  fh>m  those  found  in  other  pipes. 

Jannaiy  7th,  1874.— Prof.  Bamsay,  Y£XJA^  Yioa-Pie«dent, 
in  the  Chair. 

The  following  communications  were  read : — 

1.  "  The  Origin  of  some  of  the  Lake-basins  of  Cumberland.'* 
— First  Paper.    By  J.  Clifton  Ward,  Esq.,  P.G.S.,  Assoc.  E.S.M. 

After  rearing  to  the  fkct  that  the  question  of  the  origin  of  lake- 
basins  cannot  be  satisfactorily  discussed  unless  the  depth  of  the 
lakes  and  the  heights  of  the  mountains  are  brought  before  the 
ndnd'is  eye  in  their  natural  proportions,  the  author  sketched  out  the 
physical  geography  of  the  lakes  under  discussion  (Perwentwatery 


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312  GeohffuuU  Society: — 

Bassenthwaite^  Buttennere,  Gnunmooky  and  Loweswater),  and 
pointed  out  what  must  have  beeft  their  original  edse  and  shape 
before  they  were  filled  up  to  the  extent  they  now  are.  These  lakes 
were  not  moraine-dammed^  but  true  rock-basins.  The  belief  that 
the  present  Lake-district  scenery ^was  the  result  of  the  sculpturing 
of  atmospheric  powers,  such  as  we  see  now  in  operation,  varied  by 
dimatal  changes  and  dianges  in  the  height  of  the  district  above  the 
sea,  was  enforced,  and  the  opinion  given  that  the  work  of  elabora^ 
tion  of  the  lake-country  scenery  has  been  going  on  ever  since  Gar- 
boniferous  or  pre-Carboniferous  times.  The  lake-hollows  repre- 
sented almost  the  last  rock-shavings  removed  by  Nature's  tools. 
What  were  the  special  tools  producing  these  hollows  ?  Th^re  being 
no  evidence  of  ^eir  production  by  marine  action  or  by  running 
water,  since  they  do  not  lie  in  syndin^  troughs,  nor  along  lines  of 
Assuring  and  faulting,  and  cannot  be  supposed  to  be  speciid  areas  of 
depression,  it  remained  to  see  how  far  Professor  Eunsay's.  theory 
accounted  for  their  origin.  The  oourse  of  the  old  Borrowdale 
glacier  was  then  fully  traced  out,  and  the  power  the  numerous 
tributary  glaciers  had  of  helping  to  urge  on  the  ice  over  the  long 
extent  of  flat  ground  from  Seathwaite  to  the  lower  end  of  Bsssen- 
thwaite  Lake,  commented  on. .  The  same  was  done  with  regard  to 
the  Bultermere  and  Lreton  glacier,  and  the  depths  of  the  lakes, 
width  and  form  of  the  valleys,  and  thickness  of  the  ice  shown  by 
numerous  transverse  and  longitudinal  sections  drawn  to  scale. 
When  all  the  evidence  was  considered — the  fact  of  the  lake-hoUows 
under  examination  being  but  long  shallow  troughs,  the  thickness 
of  the  ice  which  moved  along  the  valleys  in  which  the  lakes  now 
lie,  the  agreement  of  the  deepest  parts  of  the  lakes  with  the  points 
at  which,  from  the  confluence  of  several  ice-streams  and  the  nar- 
rowing of  the  valley,  the  onward  pressure  of  the  ice  must  have  been 
greatest — the  conclusion  was  arrived  at  that  Prof.  Bamsay's  theory 
was  fully  supported  by  these  cases,  and  that  the  immediate  cause  of 
the  present  lake-basins  was  the  onward  movement  of  the  old 
glaciers,  ploughing  up  their  beds  to  this  slight  depth.  It  was 
pointed  out  dat  since  the  general  form  of  tiie  Buttermere  and 
Grummock  valley  was  that  of  a  round-bottomed  basin,  as  seen  in 
transverse  section,  the  effect  of  the  ice  was  merely  a  slight  deepen- 
ing of  the  basin  or  the  formation  of  a  smaller  basin  of  similar 
form  at  the  bottom  of  the  larger ;  whereiis  in  the  case  of  the  Der- 
wentwater  and  Bassenthwaite  valley,  which  in  transverse  section 
was  a  wide  flat-bottomed  pan,  the  action  was  to  form  long  shallow 
grooves  at  the  bottom  of  the  pan.  This  consideration  was  thought 
to  explain  the  fact  of  the  greater  depth  of  Buttermere  and  C^m- 
mock  than  of  Derwentwater  and  Bassenthwaite,  although  the  size  and 
thickness  of  the  old  glacier  in  the  former  case  was  probably  less 
than  in  the  latter.  Li  conclusion,  the  author  stated  that  he  hoped 
to  test  the  results  obtained  in  these  cases  by  bringing  forward  in  a 
foture  paper  like  details  of  Wastwater  and  other  lakes  and  moun- 
tains in  the  district. 


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On  a  great  Ice-sKeet  in  this  Lake^dktrUt.  818 

2.  <<  On  the  Traces  of  a  Great  loe-sheet  in  the  Sonthem  part  of 
the  Lake-district  and  in  North  WaleeJ''  By  D.  Maddntoeh,  Esq.. 
P.G.S. 

In  this  pap^r  the  author  brought  forward  the  eyidence  which 
seems  to  him  to  establish  the  existence  in  the  sonthem  part  of  the 
Lake*district  of  a  *<  valley-ignoring  and  ridge-concealing  ice-sheef 
With  regard  to  ice-marks,  he  distingnished  between  primary  strias 
and  those  produced  at  a  subsequent  period,  and  stated  that  in  the 
Lake-district  the  direction  of  the  primary  strife  generally  coincides 
with  that  of  the  action  by  which  nKhes  mou^onneM  have  been  pro- 
duced. He  gave  a  table  of  the  direction  of  ice-marks  observed  by 
him  in  the  district  under  notice,  and  stated  that  about  Windermere 
and  Ambleside  the  general  direction  is  nearly  N.N.W.,  round  Gras- 
mere  between  N.W.  and  N.N.W.,  north-west  and  west  of  Grasmei^ 
in  upland  valleys  and  on  high  ridges  about  N.  30^  W.,  south  of  Gras- 
mere  and  in  Great  Langdala  N.  35^  W.,  and  in  the  Coniston  district 
a  little  W.  of  N.  In  many  places  he  recognized  an  uphill  march  of 
the  ice.  He  thought  that  the  iceflow  producing  these  marks 
might  be  anterior  to  the  flow  from  south  to  north,  of  which  traces 
are  observed  in  the  northern  part  of  the  Lake-district,  and  that 
its  source  was  probably  a  vast  mass  of  ice  covering  many  square 
miles  of  country  north  of  Far  Easdale.  The  author  also  referred  to 
the  glaciation  of  North  Wales,  some  of  the  marks  of  which,  observed 
by  him  in  a  district  south  of  Snowdon,  seemed  to  him  to  indicate  the 
southerly  movement  of  a  great  ice-sheet  capable  of  ignoring  or 
crossing  deep  valleys.  He  noticed  that  towards  the  top  of  the  pass 
of  lianberis  there  is  a  thin  covering  of  drift  on  the  8.W.  side, 
resembling  the  gravelly  pinnel  of  the  Lake-district.  He  also  men- 
tioned the  occurrence  near  Llyn  Ilydan  of  numerous  mounds 
composed  of  clay,  sand,  and  fine  gravel,  the  stones  having  generally 
been  rolled  by  water,  and  ascribed  their  formation  to  a  combination 
of  glacial  and  marine  actions. 

8.  '<  Notes  on  some  Lamellibrandis  from  the  Budleigh-Saltcrton 
Pebbles.*'    By  Arthur  Wyatt  Edgell,  Esq.,  F.G.8. 

In  this  paper  the  author  commenced  by  noticing  the  accordance 
between  many  of  the  pebbles  of  Budleigh  Salterton  and  beds  occur- 
ring on  the  opposite  side  of  the  channel  in  Brittany,  and  then  de- 
scribed several  species  of  Lamellibranchiata  found  in  the  Budleigh- 
Salterton  pebbles.  The  species  described  were : — ModiolopsU  ar- 
morioi  (Salter),  M.  Lebeseontiy  sp.  n.,  Sangumalites  ?,  sp.  (contartus  ?, 
Salter),  Avieulopecien  Tromelini^  sp.  n.,  Fterinasa  retrofleaa  (Hi- 
singer)  and  three  other  species,  Pdlcearca,  sp.^  Avicula,  sp.,  Okido^ 
pTwrw?,  sp.,  Lunvloeardvum  ventricomtni  sp.  n.,  CkfMdonta^  sp.,  and 


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C    81*    ] 
XLY.  InielSgenoi  and  MUeithneoui  Artklm. 

ON  THE  ACTION  OF  TWO  SLBMENTt  Of  A  CU&&1NT. 
BT  jr.  BBBTAAND. 

««rnwO  p«nM  owrents  ftttnoi  one  isotiier  when  tbej  ]mm  iba 

are  oppoeite^"  After  enunfliatnig  this  rule,  Ampiae  beliered  hm 
could  immediatelj  ^^lenJiae  it  bj  extending  it  to  the  elemantt  of 
the  correntfl^  to  which  he  i^plm^  wheterer  nuij  be  thcdr  rdaim 
direction,  the  ide*  of  a  coune  in  the  latne  or  in  opposite  directicns^ 
Two  currenis  ue  Mid  to  be  in  the  aame  direction  iriien  they  boUi 
increaBC  their  distance  from  the  foot  of  the  common  perpendiciihr» 
oar  when  thej  both  approach  it;  in  the  contruy  cases  thejr  hare 
di&rent  directions.  Adoptang  this  kngoage,  it  is  not  aocozate  to 
sav  that  two  elements  haying  the  same  diroction  attract  one  the 
other;  it  is  not  accurate eren  for  parallel  elements.  As  theasser* 
tion  l»s  been  reprodnced  in  all  the  treatises  on^jsics,  and  senrea 
as  a  basis  for  sereral  important  e^lanations,  I  haye  thought  it 
would  be  important  to  show  tiiat  it  is  inconsistent  with  Ampere's 
law  itself,  and  to  solve  the  following  problem : — 

GKyen  an  element  oi  a  current,  to  nnd  in  a  point  M  of  space  tte 
diredion  whidi  must  be  assigned  to  another  ekmeiit  in  order  that 
thttr  mutual  action  may  be  attractire,  repellent,  or  nil. 

Suppose  the  dement  d*  placed  at  the  origin  of  the  ooordinateB 
and  diiected  along  the  axis  of  the  X's,  let  us  seek  the  condition  on 
whidi  an  element  whose  coordinates  are  ^,  y',  2^  will  be  without 
acti<mon<2f.  Namina  the  angles  formed  by  the  two  elements  inth 
the  straight  line  which  joins  them  d  and  a ,  and  ihe  an^  which 
they  make  with  one  anouier  «,  according  to  the  law  of  Ampere  the 
condition  is, 

cose=|cosdcos^ (l) 

But,  naming  the  radius  yector  1*,  and  the  atbiMsting  element  ds',  we 
haye 

^     af  ^     dr  dad 

COSe«-,      COSa^acTj,      COSCB^. 

Equation  (1)  becomes 


r 


^    ""U 


of  which  the  integnd  is 

i^^hji^, (3) 

the  equation  of  a  sur&ce  of  reyolution  wh